In a G P consisting of positive terms , each term equals the sum of the next two terms - Maths - Sequences and Series

Question

In a G P consisting of positive terms , each term equals the sum of
the next two terms Then the common ratio of this progression
equals

a) 1/2 (root 5) b) root 5 c) 1/2 (root 5 - 1) d) 1/2 (1- root 5 )

Pranjal Patel · Answer

correct option is c root 5-1/2
SOLUTION
LET THE TERM OF GP BE A ,AR, AR2, AR ^N-1
ACCORDING TO QUESTION
A=AR+AR2
A=A(R+R2)
1=R+R2
R2+R-1 SOLVE FOR R YOU WILL GET ROOT 5-1 USING D FORMULA

In a G.P. consisting of positive terms , each term equals the sum of the next two terms. Then the common ratio of this progression equals... a) 1/2 (root 5) b) root 5 c) 1/2 (root 5 - 1) d) 1/2 (1- root 5 )

In a G.P. consisting of positive terms , each term equals the sum of the next two terms. Then the common ratio of this progression equals...

a) 1/2 (root 5) b) root 5 c) 1/2 (root 5 - 1) d) 1/2 (1- root 5 )