In A G.P. of positive terms, any term is equal to the sum of... | MATH - GEOMETRIC PROGRESSION | SolveeIt | Solveeit

Today, August 18

Question

In A G.P. of positive terms, any term is equal to the sum of the next two terms. The common ratio of the G.P. is –

A

$\frac { - 1 \pm \sqrt { 5 } } { 2 }$

B

$\frac { - 1 - \sqrt { 5 } } { 2 }$

C

$\frac { - 1 + \sqrt { 5 } } { 2 }$

D

None of these

Answer

None of these

Explanation

Solution

a = ar + ar² Ž r² + r – 1 = 0

r = –1± $\sqrt { 1 + 4 }$ /2

Ž r = – 1 – $\sqrt { 5 }$ / 2, – 1 – $\sqrt { 5 }$ / 2