For a GP with first term and common ratio

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

Problem

For a GP with first term

a

and common ratio

r\,(\neq 1)

, let

S_n

denote the sum of its first

n

terms. A new GP is obtained by multiplying every term by a positive constant

7

. Let

S_n'

be the sum of the first

n

terms of this new progression. (i) Show that

S_n' - S_n = 6S_n

for every positive integer

n

. (ii) If

a = 4

and

r = \dfrac{3}{2}

, determine the least positive integer

n

for which

S_n' - S_n > 10000.