Question

If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8^th terms is ______.

Options

• 15:8

• 8:13

• 11:6

• 5:17

Answer 1

If the ratio of the sum of n terms of two AP' sis 2n:(n + 1), then ratio of their 8^th terms is 15:8.

Explanation:

∵ S_n = `n/2[a + (n - 1)d]`

`s_(n_1)/(s_(n_2)) = (n/2[2a_1 + (n - 1)d_1])/(n/2[2b_1 + (n - 1)d_2]) = (2n)/(n + 1)`

⇒ `(a_1 + ((n - 1))/2 d_1)/(b_1 + ((n - 1))/2 d_2) = (2n)/(n + 1)`  ...(1)

For T₈ we know `(n - 1)/2` = 7

⇒ n = 15

Put n = 15 in (1) we get,

`(T_8)_1/(T_8)_2 = 30/16 = 15/8`