# Finding Common Difference and Number of Terms Using Sum of N terms Formula of Arithmetic Sequence

Finding Common Difference and Number of Terms Using Sum of N terms Formula of Arithmetic Sequence

In previous video lesson we had learn to find the sum of an arithmetic progression if we don’t get the number of terms in the Arithmetic progression.

Now in this video lesson we are going to find the common difference and number of terms of an arithmetic progression using sum of n terms formula. In this exercise we have get the first term (a), last term (l ) and sum of the arithmetic progression. Now, how to find the common difference and number of terms of the arithmetic progression?

So let’s begin our video lesson of arithmetic progression. I hope you are sitting with pen and notebook.

Well how was it dear?

Yes in such problems we need to use both the formula of sum of AP that are given as below

1. S = n[2a + (n-1).d] / 2

2. S = n(a+l)/2

where a= first term of AP

n = last term

d = common difference

l = last term

Since we have not got the value of n & d we can use the first formula initially so we have to prefer second formula . Because we know the S, a and l. So we will get the value of n from there.

Steps to Solve

1. Put all the information given of the Arithmetic progression in second formula of AP.

2. Solve it and you will get the value of n.

3. Now, put all the information we have gathered into first formula we can easily get the common difference solving the relationship.

I hope you understand how to solve the problem.

Here I have listed some similar types of exercises please try to solve them. If you feel any problem comment below.

Q1. Find the sum of : 2 +4 + 6 + …………………………………+ 200. (Ans = 10100)

Q2. Find the Sum of : – 5 – 8 – 11 ………………………………………… – 230. (Ans = – 8930)

Q 3. Find the sum of : 7 + 10½ + 14 + ………………….. + 84 (Ans = 2093/2)script type=”text/javascript”>

## Comments