Answer
$\dfrac{1}{2},\dfrac{2}{5},\dfrac{2}{7},\dfrac{8}{41},\dfrac{8}{61}$
Work Step by Step
We are given the sequence:
$\{s_n\}=\left\{\dfrac{2^n}{3^n+1}\right\}$
Determine the first 5 terms of the sequence by substituting 1, 2, 3, 4, 5 for $n$:
$s_1=\dfrac{2^1}{3^1+1}=\dfrac{2}{4}=\dfrac{1}{2}$
$s_2=\dfrac{2^2}{3^2+1}=\dfrac{4}{10}=\dfrac{2}{5}$
$s_3=\dfrac{2^3}{3^3+1}=\dfrac{8}{28}=\dfrac{2}{7}$
$s_4=\dfrac{2^4}{3^4+1}=\dfrac{16}{82}=\dfrac{8}{41}$
$s_5=\dfrac{2^5}{3^5+1}=\dfrac{32}{244}=\dfrac{8}{61}$
