In a G.P. of positive terms if any terms is equal to the sum of next tow terms, find the common ratio of the G.P.

Options

A. `(sqrt(5)-1)/(2)`
B. `(sqrt(5)+1)/(2)`
C. `-(sqrt(5)+1)/(2)`
D. `(1-sqrt(5))/(2)`

Answer

A

Explanation

We have,
Let `a_(1),a_(2),a_(3), . . . . .,a_(n), . . . .` be a G.P. with common ratio r. Then,
`a_(n)=a_(n+1)+a_(n+2)` [Given]
`rArr" "a_(1)r^(n-1)=a_(1)r^(n)+a_(1)r^(n+1)`
`rArr" "r^(-1)=1+r`
`rArrr^(2)+r-1=0rArrr=(-1pmsqrt(5))/(2)rArr=(sqrt(5-1))/(2)[becausergt0"(given)"]`