Which one of the following gives the sum of the first terms of a geometric…

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

Problem

Which one of the following gives the sum

S_n

of the first

n

terms of a geometric progression whose first term is

a

and common ratio is

r\,(r\neq1)

? (a)

\displaystyle \frac{a\bigl(1-r^{\,n-1}\bigr)}{1-r}

(b)

\displaystyle \frac{n}{2}\,[2a+(n-1)r]

(c)

\displaystyle \frac{a\bigl(r^{\,n}-1\bigr)}{r-1}

(d)

\displaystyle \frac{a\bigl(r^{\,n+1}-r\bigr)}{r-1}