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Question

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms form (n+1)th to (2n)th term is 1rn.

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Solution

Sum of first n terms,

Sn=a(1rn)1r

Sum of terms from (n+1)th to 2n th term is,

S2nSn

=a(1r2n)1ra(1rn)1r

=a(rnr2n)1r

Ratio,

=a(1rn)1ra(rnr2n)1r

=1rnrnr2n

=1rnrn(1rn)

=1rn

Hence proved.

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