Consider a finite geometric progression (GP) whose first term is and common ratio is

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Consider a finite geometric progression (GP) whose first term is

a

and common ratio is

r

. Let

S_n

denote the sum of its first

n

terms. (i) Derive an expression for

S_n

when

r\neq1

. (ii) Explain why the result obtained in part (i) cannot be applied when

r=1

, and state the correct value of

S_n

for this special case. (iii) A student observes that in a certain GP the sum of the first six terms equals

6a

. Just by inspecting your results in parts (i) and (ii), determine the only possible value of the common ratio and justify your answer.