Consider a geometric progression whose first term is .

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

Problem

Consider a geometric progression whose first term is

a

. (i) Prove that if the common ratio is 1, then the sum of the first

n

terms is

na

. (ii) When

a=5

and the common ratio is 1, the sum of the first

n

terms is 40. Find

n

. (iii) Keeping

a=5

, suppose the common ratio is changed to 1.2. Determine the least positive integer

n

for which the sum of the first

n

terms exceeds 40.