Chapter 9.8, Problem 5CYU

To determine

The next three terms of geometric sequence

Answer to Problem 5CYU

The next three terms of the sequence is $160,320,640$

Explanation of Solution

Given information:

Sequence $10,20,40,80,\mathrm{...}$

Concept Used:

The equation for nth term is $a_n=a_1{\left(r\right)}^{n-1}$

The ratio is given by the formula

  $r=\frac{a_2}{a_1}=\frac{a_3}{a_2}$

Calculation:

In order to find the next three terms in the sequence simplify further as shown below,

  $\begin{array}{c}{a}_n=a_1{\left(r\right)}^{n-1}\\ a_1=10\\ r=\frac{a_2}{a_1}\\ =\frac{20}{10}\\ =2\\ a_n=10{\left(r\right)}^{n-1}\\ a_5=10{\left(2\right)}^{5-1}\\ =10\times 2^4\\ =160\\ a_6=10{\left(2\right)}^{n-1}\\ a_6=10{\left(2\right)}^{6-1}\\ a_6=10{\left(2\right)}^5\\ =10\times 32\\ =320\\ a_7=10{\left(2\right)}^{n-1}\\ =10{\left(2\right)}^{7-1}\\ =10{\left(2\right)}^6\\ =10\times 64\\ =640\end{array}$

Thus, the next three terms of the sequence is $160,320,640$