Chapter 12.3, Problem 5AYU

To determine

To find: The given statement is true or false.

Answer to Problem 5AYU

The given statement is false.

Explanation of Solution

Given information:

The given statement is.

In a geometric sequence the common ratio is always a positive number.

Calculation:

Consider a geometric sequence.

  $2,-2,2,-\mathrm{2...}$

The common ratio is given by the formula.

  $\begin{array}{c}r=\frac{T_2}{T_1}=\frac{T_3}{T_2}\\ r=\frac{-2}{2}=\frac{2}{-2}\\ r=-1=-1\end{array}$ .

Therefore, the common ratio of a geometric series can also be negative