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.
(Hint: There are two possible sets of four numbers)
+129839 a = a*r + 36 → a[ 1 - r ] = 36 → a = 36 / [ 1 - r ] (1)
ar^2 = ar^3 + 324 (2) → ar^2 [1 - r] = 324 (2)
Sub(1) into (2)
(36 / [ 1 - r ] ) r^2 [1 - r] = 324
36r^2 = 324
r^2 = 9
r = ± 3
And a = 36/ [ 1 - 3] = - 18 or a = 36 / [ 1 - -3 ] = 36 / 4 = 9
And the two series are
[ a = 9 and r = -3]
9, - 27, 81, -243 and
[ a = -18 and r = 3 ]
-18, - 54 , -162, -486
