Mathematics

Problem

A GP has first term

5

and common ratio

-2

. Every term is multiplied by

-3

to obtain another progression. a. (i) Determine the first term and the common ratio of the new progression. b. (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. c. (iii) Compute

S_5

for the original progression and

S_5'

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