Question

The sum of the first 9 terms of an AP is 81 and that of its first 20 terms is 400. Find the first term and common difference of the AP.

Answer 1

Here , a = 4 , d = 7 and l = 81

Let the nth term be 81. 

Then T_n = 81

⇒ a +(n-1) d = 4+(n-1) 7 =81

⇒ (n-1) 7=77

⇒ (n-1) = 11 

⇒ n = 12

Thus, there are 12 terms in the AP.
The sum of n terms of an AP is given by

`s_n = n/2 [ a +l]`

∴ `s_12 = 12/2 [4+81] = 6 xx85 = 510`

Thus, the required sum is 510.