Question

In an AP, the first term is 22, nth terms is -11 and sum of first n terms is 66. Find the n and hence find the4 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 off (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