Question

In an AP, the first term is 22, nth terms is –11 and sum of first n terms is 66. Find n and hence find the common difference.

Answer 1

Here, a = 22, T_n = –11 and S_n = 66 

Let d be the common difference of the given AP.

Then, T_n = –11

⇒ a + (n – 1)d = 22 + (n – 1)d = –11

⇒ (n – 1)d = –33   ...(i)

The sum of n terms of an AP is given by

`S_n = n/2 [ 2a + (n - 1)d] = 66`   ...[Substituting the value of (n – 1)d from (i)]

⇒ `n/2 [2 xx 22 + (-33)] = (n/2) xx 11 = 66`

⇒ n = 12

Putting the value of n in (i), we get:

11d = –33

⇒ d = –3 

Thus, n = 12 and d = –3