6. In a GP the 3rd term is equal to four times the first term and the sixth term is equal to three times the fourth term plus 32. Determine the sequence.

Answer 1

GP
ar^2 = 4a ----> r^2 = 4
r = ±2

ar^5 = 3ar^3 + 32

if r = +2
32a = 24a + 32
8a =32
a = 4

the sequence is 4,8,16,32,64, 128, ...

if r = -2
-32a = -24a + 32
-8a = 32
a = -4

the sequence is -4, 8, -16, 32, -64, 128, ...