Question

Find three consecutive numbers in G.P. whose sum is 28 and product is 512.

Answer 1

`a/r`, a, ar

`a/r` +  a + ar = 28

`a(1/r + 1 + r)` = 28

`a/r xx a xx ar` = 512

⇒ a³ = 512

a = 8

`8(1/r + 1 + r)` = 28

2(1 + r + r²) = 7r

2r² + 2r − 7r + 2 = 0

2r² − 5r + 2 = 0

2r² − 4r − r + 2 = 0

2r(r − 2) − 1(r − 2) = 0

(2r − 1)(r − 2) = 0

r = `1/2`, 2

1. r = `1/2`, a = 8

= `8/(1/2), 8, 8(1/2)`

= 16, 8, 4

2. r = 2, a = 8

`8/2, 8, 8(2)`

= 4, 8, 16