Q. 243.5( 72 Votes )

# Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from

(n + 1)^{th} to (2n)^{th} term is

Answer :

Let *a* be the first term and *r* be the common ratio of the G.P.

Sum of n terms =

Since there are *n* terms from (*n* +1)th to (2*n*)th term,

Sum of terms from(*n* + 1)th to (2*n*)th term =

*Here,*

*a* _{n}_{+1} = *ar*^{n+1–1} = *ar ^{n}*

∴ Required ratio =

∴ The ratio of the sum of first *n* terms of a G.P. to the sum of terms from

(*n* +1)th to (2*n*)th term is = .

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