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If the sum of an infinite decreasing G.P...

If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is `9/2,` then write its first term and common difference.

Text Solution

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Let us take a `GP` whose first term is `a` and common ratio `r`.
`:. s_(oo)y=(a)/(1-r)`
`=> a/(1-r)=3`...(1)
and, sum of the terms of the `GP=a^2,(ar)^2,(ar^2)^2, . . . oo`
...
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Knowledge Check

  • If the sum of an infinitely decreasing G.P. is 3, and the sum of the squares of its terms is 9/2, the sum of the cubes of the terms is

    A
    `(105)/(13)`
    B
    `(108)/(13)`
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    D
    none of these

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    A
    `(105)/(13)`
    B
    `(108)/(13)`
    C
    `(729)/(8)`
    D
    `(128)/(13)`

  • If the sum of an infinite G.P. be 3 and the sum of the squares of its term is also 3, then its first term and common ratio are

    A
    `3//2,1//2`
    B
    `1//2,3//2`
    C
    `1,1//2`
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