Answer
The first five terms are: $s_1 = \dfrac{1}{2}
\\s_2= \dfrac{2}{5}
\\s_3= \dfrac{2}{7}
\\s_4= \dfrac{8}{41}
\\s_5= \dfrac{8}{61}$
Work Step by Step
We are given that {$s_n$} $=\dfrac{2^n}{3^n+1}$
In order to determine the first five terms, we will have to substitute $n=1,2,3,4,5$ into the given sequence {$s_n$}:
$s_1 = \dfrac{2^1}{3^1+1}=\dfrac{2}{4} = \dfrac{1}{2}
\\s_2= \dfrac{2^2}{3^2+1}=\dfrac{4}{10} = \dfrac{2}{5}
\\s_3= \dfrac{2^3}{3^3+1}=\dfrac{8}{28} = \dfrac{2}{7}
\\s_4= \dfrac{2^4}{3^4+1}=\dfrac{16}{82} = \dfrac{8}{41}
\\s_5= \dfrac{2^5}{3^5+1}=\dfrac{32}{244} = \dfrac{8}{61}$
