Let be the first term and the common ratio of a geometric progression.

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

a

be the first term and

r\,(\neq 1)

the common ratio of a geometric progression. (a) Write the sum

S_n

of the first

n

terms in expanded form. (b) Prove that

S_n=\frac{a(r^{n}-1)}{r-1}.