Question
If 8, x, y and 27 are four consecutive terms of a GP, find the values of x and y.
Answers
oobleck
since there is a common ratio,
x/8 = y/x
y/x = 27/y
x^2 = 8y
y^2 = 27x
x^4 = 64y^2 = 64(27x)
x^3 = 64*27 = 4^3 * 3^3 = 12^3
x = 12
so, y = 18
the sequence is thus 8,12,18,27
with r = y/x = 3/2
x/8 = y/x
y/x = 27/y
x^2 = 8y
y^2 = 27x
x^4 = 64y^2 = 64(27x)
x^3 = 64*27 = 4^3 * 3^3 = 12^3
x = 12
so, y = 18
the sequence is thus 8,12,18,27
with r = y/x = 3/2