Question

If k, k + 1, and k + 3 are in G.P., then find the value of k.

Answer 1

Three terms in a GP = a, ar, ar²

a = k

ar = k + 1

kr = k + 1

⇒ r = `(k + 1)/k`

ar² = k + 3

kr² = k + 3

r² = `(k + 3)/k`

`((k + 1)/k)^2 = ((k + 3)/k)`

`(k + 1)^2/k^2 = (k + 3)/k`

(k + 1)² = k(k + 3)

k² + 2k + 1 = k² + 3k

1 = 3k − 2k

k = 1