# Proving Arithmetic Sequence from Nth term of a Sequence and Finding the Sum

In previous lessons we learn to find the sum of the arithmetic progression , some time common difference, some time we learned to find total term numbers while sometime we learned to find first term. All these we did by using the sum of arithmetic progression.

Now in this video lesson we are going to learn something different. Here we will first prove arithmetic progression after that we will find the sum of the progression.

So quickly pick the pen and notebook , let’s start our lesson.

So how are you feeling now. I hope now you are able to solve these types of problems.

Steps of Solving

1. As question has given the nth term so put the positive integers in the place of “n” and get first numbers I mean terms.

2. Check whether it is a arithmetic progression or not by checking whether common difference is constant or not.

3. Once you are sure it is A.P. now use the sum of n terms formula to find required sum given by

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

where a= first term of AP

n = last term

d = common difference

Well ! Here I have listed some similar exercises please try these all problems it will sharpen you in the topic. And if you feel any problem please comment below.

Q.1. Find the sum of first 15 term of the sequence having nth term = 3 +4n. (ans = 525)

Q2. Find the sum of first 15 terms sequence having nth term = 9 – 2n. (ans = -465)

Q3. Find the sum of first 20 terms of the sequence whose nth term = A.n + B . (Ans = 210A +20B)

Q4. Find the sum of first 25 terms of an A.P., whose nth term is given by 7 – 3n. (ans = -800)

Q5. Find the sum of first 25 terms of an A.P. whose nth term is given by 2 -3n. (ans = -925)

## Comments

## Y.Kreamudic

You are a very bright person!