Question
Question: The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then...
The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is.
A
25−1
B
21−5
C
1
D
25
Answer
25−1
Explanation
Solution
Under condition Tn=Tn+1+Tn+2
⇒arn−1=arn+arn+1⇒rn−1=rn(1+r)
⇒ r2+r−1=0⇒r=2−1±1+4=2−1±5
Since, each term is +ve.
Hence common ratio is 25−1 .