Question

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

Answer 1

Since the first three terms of a geometric sequence are $x+1$ ,$x-1$ , $x$ , the middle term must be the geometric mean of the other two. Hence

$(x-1)^2 =(x+1)\cdot x$

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

$-2x-x=-1$

$-3x=-1$

$x= \frac {1}{3}$

The first term is $x+1=\frac{1}{3}+1= 1\frac{1}{3} =\frac{4}{3}$.

The second term is $x-1=\frac{1}{3}-1= -\frac{2}{3}$

The third term is $x=\frac{1}{3}$

Answer: the first three terms of a geometric sequence are $\frac{4}{3}, -\frac{2}{3}, \frac{1}{3}$