Question

Find four numbers that form a geometric progression such that the second term is less than the first by 36 and the third term is greater than the fourth term by 324.

Answer 1

The numbers are

9,-27,81, -243

-18,-54,-162,-486

Explanation:

a = first term r = common ratio

a - ar = 36

ar^2 - ar^3 = 324

a(1-r) = 36

ar^2(1-r) = 324

r^2 = 9

r = ±3

a - ar = 36

a(1 - (±3) = 36

a = 36/4 or 36/-2

a = 9 or -18

ar = 9× -3 or -18×3

= -27 or -54

ar^2 = -27×-3 or -54×3

= -81 or -162

ar^3 = -81×-3 or -162×3

= 243 or -486