3 numbers A, B, C in that order, are in geometric progression with common ratio r. Given further that A, 2B, C in that order are in arithmetic progression, determine the possible values of r.

Answer 1

a, ar, ar^2
a, a+d, a + 2d
well
2 a r = a + d
so
d = 2 a r - a = a (2r-1)
and
a + 2 d = a r^2
2 d =a(r^2-1)
so
2 d = a(r^2-1) = 2a(2r-1)
r^2-1=4r - 2
r^2- 4 r + 1 = 0