If 1, A1, A2, A3, .... An, 31 are in A. P. and A7 : An –1 = 5 : 9 then n =

(1) 28

(2) 14

(3) 15

(4) 13

Solution:

Given 1, A1, A2, A3, …. An, 31 are in A. P.

So 1+(n+1)d = 31

d = 30/(n+1)…(i)

A7 : An –1 = 5 : 9

(1+7d)/(1+(n-1)d) = 5/9

Substitute d in above equation

9(n+211) = 5(31n-29)

9n+1899 = 155n-145

2044 = 146n

n = 2044/146 = 14

Hence option (2) is the answer.

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