In a G.P of positive terms if any term is equal to the sum of the next two terms, then the common ratio of the G.P is

Options

A. `((sqrt5-1)/2)`
B. `((sqrt5+1)/2)`
C. `-((sqrt5+1)/2)`
D. `((1-sqrt5)/2)`

Answer

A

Explanation

Let 1st term of G.P. is a and common ratio is r so a , ar , `ar^2`,…… are in GP such that a>0,r> 0
Now , according to given condition a=ar+`ar^2 rArr r^2 + r-1=0 rArr r=(-1+sqrt5)/2`