If every term of a G.P with positive terms is the sum of its two previous terms, then the common ratio of the G.P is

Options

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

Answer

B

Explanation

Let a be the first term and r be the common ratio of the G.P. Then, `agt0andrgt0`.
Now,
`a_(n)=a_(n)1+a_(n-2),ngt2` [Given]
`rArr" "ar^(n-1)=ar^(n-2)+ar^(n-3)`
`rArr" "r^(2)=r+1`
`rArr" "r^(2)-r-1=0rArrr=(1pmsqrt(5))/(2)rArr r=(1+sqrt(5))/(2)" "[becausergt0]`