Mathematics

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}

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

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

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