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

Step-by-step explanation

Given

`\begin{gathered} first\text{ term}(a_1)=5 \\ common\text{ ratio\lparen r\rparen=}(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*(1)/(5)=(5)/(5)=1 \\ third\text{ }term=ar^2=5*((1)/(5))^2=5*(1)/(25)=0.2 \\ fourth\text{ }term=ar^3=5*((1)/(5))^3=5*(1)/(125)=0.04 \\ fifth\text{ }tenth=ar^4=5*((1)/(5))^4=5*(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}`