Chapter 8, Problem 45RE

To determine

To determine if the given sequence is Geometric or not -

  $5,10,20,40,\mathrm{....}$

Answer to Problem 45RE

Thegiven sequence is a Geometric Sequence with common ratio as $2$ .

Explanation of Solution

Given:

Sequence - $5,10,20,40,\mathrm{....}$

Formula Used:

Geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence  $2,6,18,54,\mathrm{....}$ is a geometric progression with common ratio $3$ .

Calculation:

Given sequence is $5,10,20,40,\mathrm{....}$

Let $a_1=5$ , $a_2=10$ , $a_3=20$ , $a_4=40$ and so on.

  $\frac{a_2}{a_1}=\frac{10}{5}$

  $\frac{a_2}{a_1}=2$

Now,

  $\begin{array}{l}\frac{a_3}{a_2}=\frac{20}{10}\\ \frac{a_3}{a_2}=2\end{array}$ and $\begin{array}{l}\frac{a_4}{a_3}=\frac{40}{20}\\ \frac{a_4}{a_3}=2\end{array}$

Since, all the ratios are same, the given sequence is a Geometric Sequence with common ratio as $2$ .

Conclusion:

Hence, thegiven sequence is a Geometric Sequence with common ratio as $2$ .