Question

find the value of variables if they are in GP . a) k-5,k+1,k+4

Answer 1

Answer:

The first term in the GP is 5k+1, the third term is k+1 and the fifth term is k-2.

T1 = a = 5k+1 …(1)

T3 = ar^2 = k+1 …(2)

T5 = ar^4 = k-2 …(3)

Divide T3 by T1 to get r^2 = (k+1)/(5k+1) …(4)

Divide T5 by T3 to get r^2 = (k-2)/(k+1) …(5)

Equating r^2 in (4) and (5)

(k+1)/(5k+1) = (k-2)/(k+1), or

(k+1)^2 = (5k+1)(k-2), or

k^2 + 2k + 1 = 5k^2 - 9k - 2, or

4k^2 - 11k -3 = 0

(4k+1)(k-3) = 0

Hence k = 3

The AP is 16, 4, 2, 1 and 1/2.