A GP has first term and common ratio

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

A GP has first term

5

and common ratio

-2

. Every term is multiplied by

-3

to obtain another progression. (i) Determine the first term and the common ratio of the new progression. (ii) Derive a formula for the sum

S_n'

of the first

n

terms of the new progression and express it in terms of

n

only. (iii) Compute

S_5

for the original progression and

S_5'

for the new progression, and verify the relation between them.