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

$a_n=\frac{2^n}{n^2}$

1st term

Given:

$a_1=1$

With the formula of the sequence:

$\begin{gathered} a_1=\frac{2^1}{1^2}=\frac{2}{1}=2 \\ \\ a_1=2 \end{gathered}$

________

Second term:

$\begin{gathered} a_2=\frac{2^2}{2^2}=\frac{4}{4}=1 \\ \\ a_2=1 \end{gathered}$

____________

Third term:

$\begin{gathered} a_3=\frac{2^3}{3^2}=\frac{8}{9}\approx0.89 \\ \\ a_3=0.89 \end{gathered}$

_________

Fourth term:

$\begin{gathered} a_4=\frac{2^4}{4^2}=\frac{16}{16}=1 \\ \\ a_4=1 \end{gathered}$

-________________

Fifth term:

$a_5=\frac{2^5}{5^2}=\frac{32}{25}=1.28$