Geometric Series Find x if the numbers x 6 x5 are the terms

Geometric Series

Find x if the numbers x, 6, x-5 are the terms of a geometric series.

Solution

The numbers x, 6 and x - 5 are terms of a geometric series. The consecutive terms of a geometric series have a common ratio.

(x - 5)/6 = 6/x

=> x(x - 5) = 36

=> x^2 - 5x = 36

=> x^2 - 5x - 36 = 0

=> x^2 - 9x + 4x - 36 = 0

=> x(x - 9) + 4(x - 9) = 0

=> (x + 4)(x - 9) = 0

x can be -4 or 9

The value of x is (-4 , 9)