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In a G.P. of positive terms if any terms...

In a G.P. of positive terms if any terms is equal to the sum of next tow terms, find the common ratio of the G.P.

Text Solution

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Let the G.P. is,
`a, ar,ar^2,ar^3...`
Here, `a` is the first term and `r` is the common ratio.
Then, it is given that ,
`ar+ar^2 = a`
`=>r+r^2 = 1`
`=>r^2+r-1 = 0`
`=> r = (-1+-(sqrt(1-4(-1)(1))))/2 =+- (sqrt5-1)/2`
...
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Knowledge Check

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