Maths: Geometric sequence help?

Question

If x+1 ; x-1 and x are the first three terms of a geometric sequence, find x and the first three terms. Thank you in Advance

Answer 1

Geometric series is a,ar,ar^2,ar^3,ar^4...ar^n.

We know that common ratio r = t2/t1

common rato is equal.

Given (x-1),(x+1),(x) are in geometric series.

we can able to write (x-1)/(x+1) = x/(x-1)

Cross multiplication.

(x-1)^2 = x(x+1)

x^2+1-2x = x^2+x

Bring all terms to one side.

x^2+1-2x-x^2-x = 0

-3x+1 = 0

Subtract 1from each side.

-3x+1-1 = 0-1

-3x= -1

Divide to each side by negitive 3.

-3x/-3 = -1/-3

x = 1/3

First three terms are

x+1 = 1/3+1 = 4/3

x-1 = 1/3-1 = -2/3

x = 1/3