Question

Find the 4 terms in G.P. in which the 3rd term is 9 more than the first term, and the 2nd term is 18 more than the 4th term.

Answer 1

Four terms of a GP = a, ar, ar², ar³

ar² = a + 9

a(r² − 1) = 9   ....(1)

ar = ar³ + 18

ar(1 − r²) + 18

ar(1 − r²) = 18

− ar(r² − 1) = 18   ....(2)

(2) by (1)

`(− ar(r^2 − 1))/(a(r^2 − 1)) = 18/9`

`(− ar(r^2 − 1))/(a(r^2 − 1)) = 2`

r = −2

Substitute the value r = −2 into Equation 1.

a((−2)² − 1) = 9

a(4 − 1) = 9

a(3) = 9

a = `9/3`

a = 3

Four terms of the GP are 3, −6, + 12, − 24.