Question

Write the next four terms of the geometric sequence, given the first term and common ratio. If your term is not an integer type it as a decimal rounded to the nearest thousandth.a_1= 5 and r= \frac{1}{5} a_2=Answera_3=Answera_4=Answera_5=Answer

Answer 1

Explanation

Given

$\begin{gathered} first\text{ term}(a_1)=5 \\ common\text{ ratio\lparen r\rparen=}\frac{1}{3} \end{gathered}$

We can find the next four terms of the geometric sequence below;

Steps

The next four terms can be written as;

$\begin{gathered} second\text{ }term=ar=5\times\frac{1}{5}=\frac{5}{5}=1 \\ third\text{ }term=ar^2=5\times(\frac{1}{5})^2=5\times\frac{1}{25}=0.2 \\ fourth\text{ }term=ar^3=5\times(\frac{1}{5})^3=5\times\frac{1}{125}=0.04 \\ fifth\text{ }tenth=ar^4=5\times(\frac{1}{5})^4=5\times\frac{1}{81}=0.008 \end{gathered}$

Answer

$\begin{gathered} a_2=1 \\ a_3=0.2 \\ a_4=0.04 \\ a_5=0.008 \end{gathered}$