Question

The fourth term of a Geometric Progression is 48 and the sixth term is 12. Find the

possible values of the common ratio and the corresponding values of the first term.

Answer 1

Common ratio = 1/2 and first term = 384

or common ratio = -1/2 and first term = -384.

Explanation:

T6/T4 = r^5 / r^3 where r = the common ratio and T6 and T4 are 6th and 4th terms

r^5 / r^3 = 12/48

r^2 = 1/4

so r = +/- 1/2.

The 4th term = a r^3 where a = first term.

If r = 1/2:-

48 = a *(1/2)^3 = a/8

a = 8*48

= 384.

if r = -1/2, then a = -384