Question

The first term of an A.P. is 22, the last term is –6 and the sum of all the terms is 64. Find the number of terms of the A.P. Also, find the common difference.

Answer 1

First team (a) = 22

Last term (a_n) = – 6

Sum of n terms (S_n) = 64

a_n = – 6

a + (n – 1) = – 6

22 + (n – 1)d = – 6

(n – 1)d = – 28  ...(1)

S_n = 64

`n/2(a + a_n)` = 64

`n/2(22 - 6)` = 64

n = `(64 xx 2)/16` = 8

∴ Number of terms is 8.

From equation (1)

(n – 1)d = – 28

7d = – 28

∴ d = – 4

Common difference = – 4.