Answer
The first five terms are:
$a_1 = 2$
$a_2 = 4$
$a_3 = 2$
$a_4 = 4$
$a_5 = 2$
The terms do not have a common difference so the sequence 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.
$a_1 = 3+(-1)^1(1) = 3+(-1)(1) = 3+(-1) = 2$
$a_2 = 3+(-1)^2(1) = 3+(1) = 3+1 = 4$
$a_3 = 3+(-1)^3(1) = 3+(-1)(1) = 3+(-1) = 2$
$a_4 = 3+(-1)^4(1) = 3+1(1) = 3+1 = 4$
$a_5 = 3+(-1)^5(1) = 3+(-1)(1) = 3+(-1) = 2$
A sequence is arithmetic if there exists a common difference among consecutive terms. The terms do not have a common difference.
Thus, the sequence is not arithmetic.
