Question

In an AP, the first term is 2, the last term is 29 and the sum of all the terms is 155. Find the common difference.

Answer 1

Let d be the common difference.

Given:

first term = a = 2

last term = l = 29

Sum of all the terms = S_n = 155

S_n = n/2[a + l]

155 = n/2[2 + 29]

n = 10

There are 10 terms in total.

Therefore, 29 is the 10th term of the AP.

Now, 29 = a + (10 – 1)d

29 = 2 + 9d

27 = 9d

d = 3

The common difference is 3.