For a geometric progression with first term and common ratio

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

Problem

For a geometric progression with first term

3

and common ratio

2

, let

S

be the sum of its first four terms. Another progression

A

is formed by multiplying each term by

5

, and progression

B

is formed by dividing each term by

5

. If

S_A

and

S_B

denote the sums of the first four terms of

A

and

B

respectively, find the value of

\dfrac{S_A-S_B}{S}

. (a)

24

(b)

\dfrac{24}{5}

(c)

\dfrac{26}{5}

(d)

5