# Finding Sum of N terms of an Arithmetic Sequence if Number of Terms not Given

## Finding Sum of N terms of an Arithmetic Sequence if Number of Terms not Given

In previous video lesson of arithmetic progression we learn how to find the sum of natural numbers or positive integers. I hope you are good there.

Now in this video lesson arithmetic progression we are going to learn how to find the sum of an arithmetic progression if we get the last term (l) and first term (a).

Since we don’t know the total number of terms in the arithmetic progression it is really difficult to find the sum of such AP by using the formula of sum of n terms i.e.

Sum of AP = {n(n+l)} /2

Where, n = number of terms in Arithmetic progression

a = first term of Arithmetic progression

l = last term of Arithmetic progression

So let’s learn how to solve such problem. I hope you are sitting with pen and notebook.

Great ! how you feeling now?

I hope you understand now how to find the sum of such arithmetic progression when we don’t get total number of terms.

Steps to Find Sum

1. Apply nth term formula of arithmetic progression ( nth term of AP = a + (n-1)d ) for last term .

2. Solve the relation of 1 you will get the total numbers of terms in that arithmetic progression.

3. Now you know all thing i.e. first term (a), last term (l), total number of terms (n). use this information on sum of arithmetic progression formula mentioned in the top of the article.

4. Solve the relation of 3 ,you will get the sum of the Arithmetic progression you need.

Generally in this type of problem, as the formula contains 4 quantities that are a, l , n and Sum (Sn) so mostly you will get any three quantities and you have to find the fourth one. But depending on situations you may get sometime common difference as in above problem. And you have to find the sum after finding the total number of terms.

Well ! Here are few exercises related to sum of arithmetic progression formula. Try these all. If you feel any problems please comment below. I will try to get back to you.

Q1. How many terms of arithmetic sequence 18, 16, 14,……….should be taken so that their sum is zero? (Ans = 19)

Q2. If the sum of a certain number of terms starting from first term of an arithmetic progression 25, 22, 19, …………………….is 116. Find the last term. (Ans = 4)

Q3. Findthe sum of n terms of an Arithmetic progression whose nth term is given by

Nth term = 5 – 6n. (Ans = n (2-3n)

Q4. The first term and the last terms of an Arithmetic progression are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum? (Ans = 38, 6873)

Q5. The first term of an Arithmetic progression is 2 and the last term is 50. The sum of all the terms of AP is 442. Find the common difference? (Ans = 3)

Q6. How many terms of Arithmetic sequence 9, 17, 25 ,………….must be taken so that their sum is 636? (Ans = 12)

Next post you will find solution similar to above post too.

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