Answer
The first five terms are:
$a_1 = \dfrac{1}{3}$
$a_2 = \dfrac{1}{5}$
$a_3 = \dfrac{1}{7}$
$a_4 = \dfrac{1}{9}$
$a_5 = \dfrac{1}{11}$
The sequence has no common difference so it is not arithmetic.
Work Step by Step
Find the first five terms by substituting 1, 2, 3, 4 and 5 to $n$ in the given formula.
$a_1 = \dfrac{1}{1+2(1)} = \dfrac{1}{1+2}=\dfrac{1}{3}$
$a_2 = \dfrac{1}{1+2(2)} = \dfrac{1}{1+4}=\dfrac{1}{5}$
$a_3 = \dfrac{1}{1+2(3)} = \dfrac{1}{1+6}=\dfrac{1}{7}$
$a_4 = \dfrac{1}{1+2(4)} = \dfrac{1}{1+8}=\dfrac{1}{9}$
$a_5 = \dfrac{1}{1+2(5)} = \dfrac{1}{1+10}=\dfrac{1}{11}$
A sequence is arithmetic if there exists common difference among consecutive terms. The sequence has no common difference so it is not arithmetic.
