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.

The numbers are

9,-27,81, - 243

-18,-54,-162,-486

Step-by-step 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