Chapter 12.3, Problem 82AYU

To determine

To find: The value of $x$ .

Answer to Problem 82AYU

The value of x is $2$ .

Explanation of Solution

Given information:

The given consecutive of geometric sequence are $x-1,x\text{ and }x+2$ .

Calculation:

Calculate the sequence,

The ration must be the same of both sequences.

The common ratio $\left(r\right)$ is the ratio of any two successive term.

  $r=\frac{x}{x-1}\mathrm{.................................}\left(1\right)$

Also,

  $r=\frac{x+2}{x}\mathrm{.................................}\left(2\right)$

Equate the equation $\left(1\right)$ and $\left(2\right)$ ,

  $\begin{array}{c}\frac{x}{x-1}=\frac{x+2}{x}\\ x^2=\left(x-1\right)\left(x+2\right)\\ x^2=x^2+x-2\\ x=2\end{array}$

Therefore, the value of $x$ is $2$ .