Let a geometric progression have first term (a ) and common ratio (r 1 ).

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let a geometric progression have first term

a

and common ratio

r\neq 1

. (i) Prove that the sum of the first

2n

terms, denoted by

S_{2n}

, can be expressed as

S_{2n}=S_n+r^{n}S_n

, where

S_n

is the sum of the first

n

terms. (ii) Using the above relation, obtain a simplified formula for

S_{2n}

in terms of

a

r

and

n

. (iii) A geometric progression has

a=3

and

r=2

. Using your result from part (i), calculate the sum of the first 12 terms without evaluating each term individually.