Question

If n AM's are inserted between 1 and 31 and ratio of 7^th and (n – 1)^th A.M. is 5:9, then n equals ______.

Options

• 12

• 13

• 14

• 15

Answer 1

If n AM's are inserted between 1 and 31 and ratio of 7^th and (n – 1)^th A.M. is 5:9, then n equals 14.

Explanation:

d = `30/(n + 1)`

∵ `(1 + 7d)/(1 + (n - 1)d) = 5/9`

⇒ `(1 + 7  30/(n + 1))/(1 + (n - 1) 30/(n + 1)) = 5/9`

Solving we get

146n = 2044

⇒ n = 14