The sum of the first five terms of a geometric progression is 31 and its fifth term is 16.

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

Problem

The sum of the first five terms of a geometric progression is 31 and its fifth term is 16. (i) Denote the first term by

a

and the common ratio by

r

. Write expressions for the fifth term

T_5

and the sum of the first five terms

S_5

in terms of

a

and

r

. (ii) Using the information given in the question, obtain two simultaneous equations in

a

and

r

. (iii) Solve the equations obtained in part (ii) to determine the values of

a

and

r