An AP and a GP both have first term

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

5

. The AP has common difference

3

while the GP has common ratio

2

. (i) Obtain, in simplest form, the sum of the first

n

terms of each progression. (ii) Determine the smallest positive integer

n

for which the sum of the GP exceeds the sum of the AP.