Hello everyone, welcome back to our new video.
The topic we are going to discuss in today's video is
Arithmetic Progression.
In short, we will call it AP.
What is Arithmetic Progression?
First of all, we need to know what is a sequence.
What is a sequence?
We will see the sequence of numbers in Mathematics.
Sequence means you have numbers in a proper defined pattern.
And how will those numbers come?
They will come with the help of a formula or a rule.
Suppose you have a formula given.
You should have 2n plus 1.
You have a formula given as 2n plus 1.
And here is equal to is given as an.
What is an? It is the address.
The way we will write numbers in sequence.
In a pattern, first number, then second number, third
number, fourth number and so on.
For that, you have a formula given.
an is equal to 2n plus 1.
Now, how will we get numbers from it? Where do we start the
sequence from? From the value of n, 1.
Why from 1? Because it is our first term.
So, the first term, the n denoted here, denotes the number
of terms you are writing.
Which number of terms you will find out.
So, n is your number of terms.
Obviously, the first term comes.
So, we will put the value of n as 1.
So, if we are putting the value of n as 1, then what do you
have in front of a1?
You have 2.
Where there is n, you will replace n with 1.
Because we are taking the value of n as 1.
So, a1 is equal to 2.
Instead of n, we have 1.
So, 2 into 1 plus 1.
That is 2 into 2 is 2 plus 1 is 3.
This is your first term of a sequence.
Similarly, if you have a defined formula, you can find out
the second term.
Now, what is the value of n to find out a2? 2.
So, 2 into 2 plus 1.
That would be 4 plus 1 is 5.
Then, a3.
What will a3 be? 2 into 3.
That is 6.
And 6 plus 1.
6 plus 1 is 7.
And then so on.
You can find out all the values in front of a3.
So, if you write these numbers line wise.
The first number is coming order wise.
The first number is a1.
First, you will write a1.
Then, the second term is a2.
Then, a3.
And then so on.
It will keep on increasing.
You can keep on adding as many terms as you want.
So, you will keep a1 as 3.
Then, you will put a comma as 5.
Then, a comma as 7.
Then, a comma next term would be 9.
And so on.
It will keep on increasing.
So, this is what we call a sequence of numbers.
Now, we are talking about a sequence.
You see, 3, 5, 7, 9 and so on.
So, this is your sequence.
Now, what is the first term in this? 3.
So, these are your terms which are separating from the
comma.
What are these?
These are your terms.
So, the sequence can be of finite terms.
If we see only 4.
So, there are only 4 terms in the sequence.
So, it becomes finite.
If it keeps on increasing, there is no end of n.
You can put any value of n.
But, you don't know the last value of n.
So, numbers will keep on increasing.
So, that will become your infinite sequence.
Now, we are talking about a sequence.
Now, if you understood the sequence, then quickly do an
example.
I am giving you a new formula.
You have to denote a n with the power of 2n plus 1.
So, the first term will be 2n plus 1.
So, quickly make a sequence of this.
Let me make it.
First of all, you take n.
What should you take for n? 1 What should you take for n? 1
So, when you take n as 1, then a1 will become equal to 2.
Where n is 1, 1 plus 1 is 2 power 2.
This number will be 4.
Then, what will you do next? n is equal to 2.
For n is equal to 2, you will get a2 number.
For a2 number, the second term will be 2.
2 plus 1.
For n is equal to 2, 2 plus 1.
So, this will be 2 power 3.
That is 8.
Similarly, if you take a3, that will be 2 power 4.
That is 16.
And so on, it will keep on increasing.
Numbers will keep on increasing.
So, this will be your sequence.
So, if numbers are coming in a fixed pattern through a
formula, in which you are keeping the value of n, then you
are getting first term, second term, and so on, up to n
terms.
So, that will be your sequence.
Now, after the sequence, the next thing is series.
What will be series?
If you add the terms of the sequence and write it,
For example, you were writing it as 2, what was its first
term? 4, 8, 16.
You were writing it as 4, 8, 16.
If instead of using commas, you keep on signing plus
instead of commas, like 4 plus 8 plus 16.
Now, all these terms were of the sequence.
But we are writing them as add.
So, what is this called?
Now, this thing is called series.
So, the difference between sequence and series is that you
will separate the terms of the sequence from the commas.
In series, you will add the same terms and keep on writing.
So, we have just read the basic tool in your arithmetic
progression.
Means, somewhere, they took birth from someone.
AP is born from someone.
So, you should know the sequence.
Now, what is Arithmetic Progression?
If, like we saw this question, it had 4 in the beginning,
then you have 8, then you have 16.
So, the gap between them, like from 4 to 8, how many steps
will you reach?
You will have to cover 4 steps.
Like, 1 step from 4 to 5, then 5 to 6, 6 to 7, then 7 to 8.
So, here, you are reaching after 4 steps.
From the first term to the second term, you are reaching
after 4 steps.
Then, you are reaching after 8 to 6.
Means, from the second term to the third term, how many
steps are you reaching?
You are reaching after 8 steps.
Now, from 16 to the next number, if you put it in the
formula, then you will get 32.
From 16 to 32, how many steps will you reach?
You will reach after 16 steps.
So, these steps, between consecutive two numbers, two terms
of a sequence, in the adjacent terms of 2 and 7, if you see
the gap, then you do not have one thing. Means, it is not
common.
The gap in all of them is different.
In this, it is 4.
In this, the gap has increased to 8.
Then, the gap is increasing to 16.
And so on.
So, if we have this gap, instead of being different, it
becomes the same gap.
Like, you did the first example, 3, 5, 7, 9, and so on. In
this, you see, between 3 and 5, what is the gap?
There is a gap of 2 steps.
Similarly, between 5 and 7, there is a gap of 2. Between 9
and 7, there is a gap of 2. And so on.
If you go ahead, the gap you will get, is the same gap
between two terms. You will get the same space, which is 2.
So, when we have, in terms of a sequence, listen carefully,
when we have, in terms of a sequence, there is a gap
between two consecutive
terms.
Consecutive means, together, in the adjacent term, if you
get the same number gap, between two consecutive terms,
arithmetic progression.
Arithmetic progression
Arithmetic progression Arithmetic progression
Arithmetic progression
I hope it's visible to all.
Find the 5th term of the arithmetic progression.
Find the 5th term of the arithmetic progression. So, if you
take out a3, the value will be the same but it will be in
negative.
So, your entire question will be different in terms, being
in negative.
So, from a3, we will always minus the previous one.
So, what will be the value of d? d would be a3 minus a2 or
a2 minus a1.
You can take any of the two. If the gap is the same, then
you can take anything.
Now, what is a3? It is 5. So, 5 minus 1 is 4.
There is a gap of 4.
Similarly, if you take 1 minus of minus 3, then what will
happen? 1 minus of minus 3.
1 plus 3, that is 4.
So, the gap should have been the same in both.
It is the same, which is 4.
So, you got the value of d as well.
So, a has come, a is there, d is there, n is also there.
So, take out the fifth term.
So, what will be a5? a5 is equal to a, the value of a is
minus 3, plus n minus 1, that is 5 minus 1.
The value of d is 4.
So, what has come? Minus 3 plus 4 into 4 is 16.
16 minus 3 is 13.
So, your fifth term will be 15.
How did you get this?
See, this is again a question of the fifth term.
So, you can do it in any way.
Instead, to solve this much, the third term is given to you.
The common difference is d.
So, if you add 4 to 5, then you get the fourth term.
Then, if you add 4 to 9, then you get the fifth term.
So, you could have taken it out from there as well.
Because now, this is a small number.
It is a question of the past only.
Because, when you have to solve in a big question, when it
is more, but in a small one, in which it takes less time,
we will obviously opt that way.
So, you can do this as well.
This question was easy, right?
Okay.
So, we have done the nth term.
Now, the next thing you have is, we have done the formula
for the nth term.
Next, you have the sequence.
Now, you had numbers in AP.
First number is A, then A plus D, then A plus 2D, plus up
to A plus N minus 1D.
This is the nth term.
It can go further or not.
So, suppose we are taking the finite sequence.
Which one? Finite AP.
We have this finite AP.
Which means, there are only terms up to AN.
Now, what we have to do is, we have to find out the sum of
all these.
What we have to find out is the sum.
Which means, if we add all these, what will we get?
We have to find out the addition of all these.
So, how will it be?
Their addition.
If you add all these, then see, A plus A plus A, how many
times is A being added?
A is being added N times.
And this D plus 2D plus, how far is it going?
Up to N minus 1D, the terms of D are being added.
So, write the direct formula of the sum.
Sum is S.
Just like we denoted the nth term as AN, similarly, the sum
of N terms of an AP.
What is this?
Sum of N terms of an AP.
What will be the formula for this?
There are two formulas for this.
First of all, you will do N by 2.
And in brackets, A plus L.
A plus L, now you will say,
Ma'am, where did this new variable come from?
L.
You all know A, the first term.
You know N, how many terms will be there.
L is the new thing.
That is your last term.
The last term will be this.
This will be your L.
You have denoted this with L.
You have denoted the last term with L.
Now, if you put this value of the last term,
A plus N minus 1D, then this formula will be N by 2, 2A, 1A
of this, and 1A of this, when you put the value of L, then
it will come.
Plus N minus 1D.
This is for when?
Suppose, if you are not given the last term, then you can
get this with the help of N, D and A.
So, this is your sum formula.
This is also important.
So, you can remember any one of these.
Obviously, the other one.
Remember the one with L.
Put the formula of the nth term in L.
You will get the formula of the sum.
Okay? Remember this quickly.
Let's see a question on this.
This is for the finite.
We will also see for the infinite.
But, for now, this is for the finite terms.
If you have a finite number of terms in AP, then what will
be the sum of them?
Okay? So, look at the question on this.
Look at this.
Find the value of 400 plus 404 plus 408 plus up to so on up
to 800.
Now, look at this.
The questioner is very smart.
He played with you.
He did not give you a language to find the sum of AP.
So, that you do not get a sudden click in your mind.
That this is AP.
Right? So, he did not make a direct question.
What did he do?
He wrote it like a sum.
Now, you will have to think about the first step.
Is this AP?
Means, you will not get a sudden click in your mind.
Is this AP or not?
If he would have given in a comma, and then he would have
said, find out their sum.
Then, you would have paid attention that this is AP.
But, now, what will you do?
First of all, you will hold this.
If we have to find the sum, then is this from AP?
We will read GP next.
GP is different.
But, is this AP?
We will check from AP or GP.
Now, let's check for AP.
So, you will see a gap in this.
This is basically nothing.
This is a sequence of AP.
In this form.
First term is 400.
Then, second term is 404.
408 up to 800.
Last term is 800.
Now, you see this AP.
These are your terms.
See their difference.
404 minus 400.
Difference of 4.
Means, If we go from 400 to 404, then we have to go for
plus 4 steps.
From 404 to 408, we have to go for plus 4 steps.
And so on, by doing 4 steps.
So, this is our common difference.
What? Common difference, value of D is 4.
Okay? You can see the value of A.
First term A is equal to 400.
And, what is this 800? 800 is your last term.
Which you have denoted by L.
800.
You have L.
What do you have?
You have value of A.
So, will you be able to find the formula for sum?
What is sum?
N by 2.
A plus L.
A plus L is A.
L is here.
N is not here.
What you have to do is, put the value of N, and you will
get the sum.
Now, how to find out N?
Whatever we have done, only that formula will be used.
No one else will be used.
Have you done the formula for AN? What is the formula for
AN?
Nth term AN is equal to
A plus N minus 1D.
Right? If we see the last term, from the last term, we will
be able to find the number of terms.
So, let us take the last term.
AN.
So, AN is equal to 800.
What is the value of A?
A is equal to 400.
You have to find out N.
What is the value of D? 4.
Will you be able to solve this? 800 minus 400. 400 is equal
to N minus 1D.
That is 4.
If you divide 4, you will get 100.
100 is equal to N minus 1.
What is the value of N? 100 minus 1 is equal to 101.
What is the value of N? 101.
Which term is 800? 101th term.
101th term.
You have A101.
Put the value of N here.
Put the value.
What will happen? N is equal to 101 by 2.
A is equal to 400.
L is equal to 800.
Solve it.
This is 1200. 1200 divided by 2 is 600.
If you multiply 600 by this, it becomes 606 and 20600.
Okay? I solved it quickly, but you can also do it.
400 plus 12.
Now, if you go to give the entrance, placement, etc., then
obviously, your math will be this strong.
So, 400 plus 800 is 1200.
Divide 1200 by 2 is 600.
Then, multiply 600 by 101.
Then, you will get the answer of sum.
Okay? Otherwise, what would you have done? You would have
taken the calculator and added all the numbers.
You wouldn't have done that, right?
That's why, math is made for your comfort.
Which we saw in the form of AP.
We got the sum quickly with the help of the formula.
Okay? So, basically, you have this in AP.
Now, we will mainly practice its questions.
So, let's see the next question.
Now, the questions that you will get in AP can mainly come
in the form of word problems.
But, you won't be able to tell that it is AP.
You will be able to tell by reading it, but you won't be
able to see it in the form of AP, comma.
So, let's see the first question.
Read it.
If the first, second, and last term of an AP are 15, 19,
and 111 respectively.
First, let's write the data that we have read from the
first line.
So, what is the first term? 15.
So, can I write A1 as 15?
If the second term is 19, can I write A2 as 19?
Now, the last term is 111.
So, what is the result of denoting the last term as AN?
We don't know what N is.
So, denote it as AN.
What is the result of 111?
We have denoted our last term as AN.
Now, find the total number of terms in the AP.
We have to tell the total number of terms in the AP from 15
to 111.
So, basically, you have to find out the value of N.
You can find it out.
In the last question, we had found N for the sum.
Then, we had gone into the formula of the sum.
So, this is one step behind.
In this, we have to find only N.
So, how will we find N?
Obviously, you have been given the value of the first term
A1.
So, both the first and second terms are consecutive.
You will find D from their difference.
So, D will be equal to 19 minus 15.
So, D will be equal to A2 minus A1.
That is, 19 minus 15 is equal to 4.
The value of D in this question is also 4.
Okay? The Nth term is 111.
So, you can use the formula of the Nth term.
What will be the formula of this?
A plus N minus 1 D is equal to 111.
Because, that is the value given.
So, put the value of D as 4.
The value of A is 15 plus N minus 1 into 4.
Now, it is solved.
Now, it is basic.
Put 15 minus here.
So, what will be this? 111 minus 15.
So, this will be 96.
This would be 96.
Divide this by 4.
So, divide by 4 is equal to N minus 1.
Divide by 2.
16 is equal to 24.
This is equal to N minus 1.
What is the value of N?
Minus 1 is here.
Plus 1 is here.
So, it is 25.
What is the total number of terms in this sequence? 25.
It took a little time to solve this.
Not much time.
It took a little time.
I have filled the board here.
But, did you see how quickly you are doing the calculation
in this?
And, it is not very tough.
There is only one formula.
And, we have one formula.
It is not very difficult.
We are increasing on the basis of that only.
Okay? We have done this question also.
Let us see the next one.
Next is, see.
The third term of an AP.
Keep writing whatever is given.
Third term of an AP.
A3 is given to you.
25.
And, the tenth term.
A10 is given to you.
Minus 3.
Find the first term and the common difference.
You have to find out the value of A.
And, you have to find out the value of D.
Till now, whatever question you have done earlier.
The example that we have just done.
In all those, you were given the value of A.
You were given from the first term.
But, what is there in this question?
A3 and 10 are given.
A10.
A value is not given.
So, how will you find out the value of A?
After the value of A, you have to find out the value of D.
So, let us see.
What will you use in this?
See, the sum was not being used till far.
So, we will use the formula of sum.
No.
Only one formula is left.
Formula of AN.
So, the formula of AN.
Write in the side, in the copy.
AN is equal to A plus N minus 1 D.
We have written.
Now, next.
Next thing.
The values that you are given.
For example, this is given for 3.
This is given for 10.
So, once you put N as 3.
Then, the formula of A3 will come.
As soon as the formula of A3 comes.
Its value is 25.
So, keep that.
So, from there, one equation will be formed.
With the help of A10, the second equation will be formed.
Okay? I am telling you, do it quickly. Okay? So, what will
we do?
First, we are putting N is equal to 3.
Where are we putting N is equal to 3?
In our Rambad formula.
In the main formula.
So, we put 3 instead of N.
So, what is formed?
A3 is equal to A plus N minus 1.
N is 3.
So, 3 minus 1 will be 2 into D.
So, you have A plus 2D is equal to 25.
Its value is 25.
So, you have one equation.
Now, with the help of A10, the second equation will be
formed.
So, we will put N.
What will we put N?
We are putting N.
Let's do it with a different pen.
So that there is some much difference.
So, we put N.
Sorry, this is not 3.
We will put N this time.
10 As soon as we put N as 10.
So, instead of N, A10 is formed.
Now, we don't know the value of A.
So, A plus N minus 1.
10 minus 1 is D.
10 minus 1 is 9.
So, A plus 9 is D.
And what is the value of A10?
Minus 3.
So, what do you have?
The second equation is formed.
Now, you have two variables and two equations.
Can you solve them?
Yes, you can.
What should you do?
Subtract the first and the second.
What should you do?
Subtract.
I will tell you by subtracting here.
A plus 2D is equal to 25.
And A plus 9D is equal to minus 3.
Subtract them.
As soon as you subtract the first equation, the sign of the
second equation will change.
Where there is plus, there is minus.
Where there is minus, there is plus.
So, A minus A is 0.
2D minus 9D is minus 7D.
And 25 is equal to minus 3.
But the sign of the second equation will change.
25 plus 3 is equal to 28.
So, what is the value of D? 28 divided by minus 7 is equal
to minus 4.
In the previous equation, D was 4, 4, 4.
But in this equation, it is minus 4.
It is 4.
But all the equations are of 4.
But D is in the negative sign.
It means that the number of sequences is decreasing.
First, A3 was 25.
Then, it decreased to A10.
The number of sequences is negative.
It means that D should have been negative.
So, D is minus 4.
Now, D is here.
So, put the value of D in any of these equations.
You will get the value of A.
I will do it in this equation.
You can do it in this equation.
In the first equation, 25 is equal to A plus 2 into D minus
4.
So, D is equal to minus 8.
A is equal to minus 8.
Now, take minus 8 with 25.
25 plus 8 is equal to 33.
So, the value of A is 33.
The first term of this sequence is 33.
What will be the value of A2?
From 33, you will add D.
It is a negative sign.
So, you will have to subtract it.
From 33, the value of D is minus 4.
So, the second term of this sequence is 29.
Then, from 29, you will subtract 4.
So, the third term of this sequence is 25.
In the question, you were given 25.
So, this answer has been verified.
There is no need to verify it in the exam.
I am just telling you that now.
Okay? So, we have done this question also.
In which, we were given the first term and some other terms.
we have found out the first term and common difference with
the help of these two variables.
Now if you want to find out both A and D, then it will give
you at least two such things, with the help of which two
equations will be created.
Because you have to find out two variables, isn't it? It
will give you some hint, with the help of which both A and
D will be solved simultaneously.
So, moving on to next question.
Is the next question same?
Yes, it is same.
Next question.
Find the sum of all the numbers between 200 and 400 which
are divisible by 7.
We have to find out the sum of all those numbers between
200 and 400, which are divisible by 7.
Now, you have to do a little extra work in this.
You have to use your brain and common sense.
Basically, you have to find out the sum of all those
numbers.
To find out the sum, obviously, which formula will you use?
You will use the formula of sum.
You have got Sn.
Write the formula of Sn as soon as you see the sum.
What was Sn? n by 2?
Either it was a plus l or a plus n minus 1 d.
Write both the formulas.
I have written both the formulas on one side.
Now, which type of numbers do you have to find?
The numbers which are between 200 and 400.
The numbers which should come in between should be
divisible by 7.
So, should we find out all the numbers divisible by 7?
Between 200 and 400.
And then we will find out the sum of all those numbers.
No.
What we need is the number of terms n, a, l and last term.
So, how will we do this?
Can you find out the first term?
Will you take the first term as 200 and l as 400?
You will not take the first term as 200.
Because the terms which should come in between should be
divisible by 7.
And 200 is not divisible by 7.
So, we will find out the number after 200.
201.
Is 201 divisible by 7?
Look at 201.
201 divided by 7.
So, 14.
How many are left? 61.
61 is not there.
So, 201 is also not there.
If you look at 202, it is also not divisible by 7.
Because 62 is not there.
So, look at 203.
203 is divisible by 7.
So, 7 times 2 is 14.
Remainder is 6.
So, 63.
Does 63 come in the table of 7? 9 times 9 is 9.
So, 203 is divisible by 7.
So, the first number will be 203.
We got the first number.
Remainder will come from the first term.
So, 7 is your A1.
Now, what should be in the table of 7?
How many will be there in the table of 7? 7.
So, what will be the second term? 7 plus 7.
That would be 210.
Then, 3rd term will be 7 plus 7.
That will be 217.
Then, 7 plus 7 will be 217.
And so on.
Can someone tell me the last term? We will do the same as
we did for the first term.
We will do the same for the last term.
It should be between 400 and 7.
So, let us check 400 first.
Is it divisible by 7?
So, check 400.
If you divide 400 by 7, you will get 35.
Then, you will not get 50.
So, if you divide 400 by 7, you will get 399.
3999.
Sorry, it is not triple. It is double 9.
So, you will get 35.
How much is left? 4.
So, you will get 49.
So, we have completely divided it.
We got 0 remainder from 47.
So, it will be 399.
The last number will be between 200 and 400.
It is divisible by 7.
So, the last number is 399.
You got A.
And you got L.
What do you want?
You have the requirement of N.
You have the right to use the formula of sum.
It is valid to use the formula of sum.
So, how will we get N?
As soon as we get the last term, we can get N.
How will you get N?
The formula of last term will be AN.
AN is equal to A plus N minus 1D.
It is the second Ram Bandhan formula.
The first formula is of second sum.
So, you are getting the last term AN.
So, 399 is equal to 203 plus N minus 1.
You have to find out the value of N.
The value of D is 203.
What will you do now?
Sorry, the value of D is not 203.
What is the value of D? 7.
7.
Now, you have N and 1 equation.
Find out the value of N.
Minus 203.
What will you get? 6.
9.
196 is equal to N minus 1D.
7 is here.
Divide 7.
What will you get? 7 times 7 is equal to 14.
2 times 14 is equal to 56.
56 is equal to 28.
What is the value of N?
Take plus 1.
The value of N is 29.
So, the total terms between 200 and 400 which are divisible
by 7 are 29 terms.
The first term starts from 203 and goes up to 399.
So, in the formula of Sum, in the formula of Sn, the value
of N is 29 divided by 2.
The first term is 203.
The last term is 399.
Add these and divide.
What will happen to 9 plus 2? 9 plus 3 is equal to 12.
1.
0.
1.
602 divided by 2 is equal to 29.
Divide 2 by 2.
301.
This is all you have to do.
Do it quickly at home.
Not at home, do it now.
You will get the formula of Sum.
Wait a second.
I hope you have done the multiplication.
Let's move to the next question.
Before doing the next question, let me tell you one thing.
If we are doing the formula of Sum, you will get the
formula of Sum of first and natural numbers.
What will you get?
Sum of first and natural numbers.
If you look at the natural numbers, we will not go into the
derivation.
It is not needed.
Why do you have to do MCQ?
The derivation is in two steps.
It is not much.
Let's look at the sum of first and natural numbers.
If you look at the natural numbers, first and natural
numbers means starting with n natural numbers.
The first natural number is 1.
Then comes 2, 3, 4 and how far do you have to go? Till n.
We have gone till n.
Now you will see one thing.
See the gap.
The gap is of plus 1.
If you do plus 1 here, you will get plus 1 here.
So where is the gap?
We have it in AP.
Because the gap is constant.
It is the same in every consecutive term.
So these are the terms of AP.
Now you have to find out their sum.
What will be their sum?
Remember the formula.
We will take n.
We will add 1 to the last term.
n plus 1.
Add 1 to the last term.
Divide by 2.
n into n plus 1.
Divide by 2.
This is also known as summation n.
Summation means plus.
This is a notation.
First, the value of n.
From i to n.
If you add 1 to the value of i.
If you add 1 to the value of n.
Sorry.
What is the value of n?
From 1 to n.
Summation n.
First, add 1.
Second, add 2.
Then, add 1 plus 2 plus 3 plus 4.
This is your sum.
You have to find out the sum.
1 plus 2 plus 3 plus 4 up to n. You can denote the sum of
all the terms by denoting the formula of summation n, which
is n into n plus 1 by 2.
This is the sum of first and natural number.
Suppose you are asked to take the sum of 1 to 1 plus 2 plus
3 plus up to 50.
So what will you do?
How far are the terms going?
You will get 50 by 2 into 51.
So 50 into 51 divided by 2 is 25 into 51.
This will be the sum of all the natural numbers from 1 to
50.
This is the addition.
I just wanted to tell you this.
Next we will move on.
Let's see how many questions are left.
Now you have 4 questions.
Let's do this.
We will do these 4 questions in next video.
Because this video is already too long.
Then you won't be able to keep it in your mind so soon.
So in next video, we will do the remaining questions.
Maybe we will do some more addition.
We will see some more formulas.
Like we saw the sum of n natural numbers.
So we can also do the sum of their square.
We will see that in next video.
Till then what you have to do?
Obviously revise these 2 formulas.
Because without these you won't be able to do AP.
And understand the example from your side.
Thank you for watching the video.
Meet you in the next video.
No, I haven't.
What's it about?
That sounds interesting.
Count me in.
I'll make sure to spread the word to all my knowns.