Question

The first three terms of the sequence -8,x,y,72... form an arithmetic sequence, while the second, third and fourth terms form a geometric sequence. Determine x and y.

Answer 1

y-x = x+8
y/x = 72/y

y = 2x+8

(2x+8)/x = 72/(2x+8)
4x^2+32x+64 = 72x
4x^2-40x+64 = 0
x^2 - 10x + 16 = 0
(x-2)(x-8) = 0
x=2,8
y=12,24

so, we have

-8,2,12,72
or
-8,8,24,72

Answer 2

thanks:-)