Question

Find the first 5 terms of the following sequence. For the first term let a_1=1. Round your answer to the nearest hundredth.a_n= \frac{2^n}{n^2} 1st term = Answer2nd term = Answer3rd term = Answer4th term = Answer5th term = Answer

Answer 1

`a_n=(2^n)/(n^2)`

1st term

Given:

`a_1=1`

With the formula of the sequence:

`\begin{gathered} a_1=(2^1)/(1^2)=(2)/(1)=2 \\ \\ a_1=2 \end{gathered}`

________

Second term:

`\begin{gathered} a_2=(2^2)/(2^2)=(4)/(4)=1 \\ \\ a_2=1 \end{gathered}`

____________

Third term:

`\begin{gathered} a_3=(2^3)/(3^2)=(8)/(9)\approx0.89 \\ \\ a_3=0.89 \end{gathered}`

_________

Fourth term:

`\begin{gathered} a_4=(2^4)/(4^2)=(16)/(16)=1 \\ \\ a_4=1 \end{gathered}`

-________________

Fifth term:

`a_5=(2^5)/(5^2)=(32)/(25)=1.28`