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Question

The 4th and 7th terms of a G.P. are 127 and 1792 respectively. Find the sum of n terms of the G.P.


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    Solution

    t4=127, t7=1792, tn=arn1

    Where tn=nth term, r = common difference, n = number of terms.

    t4=ar3=127 ....(i)

    t7=ar6=1792 ....(ii)

    Dividing (ii) by (i), we get

    t7t4=ar6ar3=r3=27729=127,

    r=13

    Sum of n term =Sn=a(1rn)1r .......(iii)

    When, r = 3, t4=ar3=127

    a(13)3=127

    a=1

    Substituting a=1, r=13 in (iii)

    Sn=1(1(13)n)113

    =1(13)n23

    =32(1(13)n)


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