in a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equ

Question

in a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equ

in a geometric progression 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)(1-sqrt(5))`
B. `(1)/(2)sqrt(5)`
C. `sqrt(5)`
D. `(1)/(2)(sqrt(5)-1)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
Let geometric progression is `a,ar,ar^(2),"…."," " [a,rgt0]`
`:.a=ar+ar^(2)`
`implies r^(2)+r+1=0 implies r=(-1pmsqrt(5))/(2)`
`:.r=(sqrt(5)-1)/(2)`.

4 views Answered 2023-02-05 15:29