Consider the geometric progression 240, 120, 60, 30

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

Problem

Consider the geometric progression 240, 120, 60, 30, \dots defined for positive integers

n

. (i) Identify the common ratio

r

and write the general term

a_n

of the progression in terms of

n

. (ii) By examining the value of

r

, explain whether the sequence of partial sums

S_n

approaches a finite limit as

n

becomes very large. Give a brief reason for your answer without explicitly using any summation formula. (iii) Calculate

S_6

, the sum of the first six terms, and comment on how its value supports the conclusion you reached in part (ii).