Mathematics

Problem

In a G.P. the product of its

3

rd and

8

th terms is

512

, while the sum of its

4

th and

6

th terms is

40

. a. (i) Form two separate algebraic equations in

a

and

r

corresponding to the given product and sum. b. (ii) Solve these equations to find the first term

a

and the common ratio

r

. c. (iii) Using the values of

a

and

r

, calculate the

10

th term of the progression.