During the derivation of the sum of the first terms of a GP with first term and…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

During the derivation of the sum of the first

n

terms of a GP with first term

a

and common ratio

r\,(r\neq1)

, one arrives at

rS_n-S_n=ar^{n}-a.

Which of the following is the correctly simplified expression for

S_n

obtained from this equation? (a)

a\dfrac{1-r^{n}}{r-1}

(b)

\dfrac{r^{n}-1}{r-1}

(c)

a\dfrac{r^{n}-1}{r-1}

(d)

a\dfrac{r^{n+1}-1}{r-1}