Question

In an A.P., if the first term a = 7, nth term a_n = 84 and the sum of first n terms `s_n = 2093/2`, then n is equal to ______.

Options

• 22

• 24

• 23

• 26

Answer 1

In an A.P., if the first term a = 7, nth term a_n = 84 and the sum of first n terms `s_n = 2093/2`, then n is equal to 23.

Explanation:

Given,

a = 7, a_n = 84 and `s_n = 2093/2`

∵ an = a + (n − 1)d

⇒ 84 = 7 + (n − 1)d

⇒ 77 = (n − 1) d    ...(1)

Also, `s_n = n/2[2a + (n - 1)d]`

⇒ `2093/2 = n/2[2 xx 7 + (n - 1)d]`

⇒ 2093 = n [14 + 77]      ...[from eq. (1)]

⇒ 2093 = 91n

⇒ n = 23