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 common ratio is ___.
Answer: Option A
:
A
The given condition can be expressed as
Tn = Tn+1+Tn+2, where n≥1.
If a is the first term and r is the common ratio, then by the condition is
arn−1=arn+arn+1.⇒rn−1=rn(1+r)
⇒r2+r−1=0
⇒r=−1±√1+42=−1±√52
Since each term is positive, the common ratio of the GP is √5−12.
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:
A
The given condition can be expressed as
Tn = Tn+1+Tn+2, where n≥1.
If a is the first term and r is the common ratio, then by the condition is
arn−1=arn+arn+1.⇒rn−1=rn(1+r)
⇒r2+r−1=0
⇒r=−1±√1+42=−1±√52
Since each term is positive, the common ratio of the GP is √5−12.
Was this answer helpful ?
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