Question

In the following exercise, determine if the sequence is geometric, and if so, indicate the common ratio.

$2,10,50,250,1250,6250,...$

Short answer

The sequence is a geometric sequence with common ratio equal to$5$.

Step-by-step solution

Step 1. Given information

The sequence is $2,10,50,250,1250,6250,...$

Step 2. Determine if the sequence is geometric and if so, indicate the common ratio. 

The sequence is said to be geometric if the ratio between consecutive terms is same.

Consider the sequence $2,10,50,250,1250,6250,...$

$\begin{array}{rcl}\frac{10}{2}& =& 5\\ \frac{50}{10}& =& 5\\ \frac{250}{50}& =& 5\\ \frac{1250}{250}& =& 5\\ \frac{6250}{1250}& =& 5\end{array}$

As the ratio between the consecutive terms is constant, the sequence is geometric with common ratio equal to$5$.