Answer
Explicit Formula: $a_{n}=10$$(-1)^{n-1}$
First five terms: $10,-10,10,-10,10$
Work Step by Step
Recall the explicit formula for a geometric sequence:
$a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$
where
$a_n$ = $n^{\text{th}}$ term;
$a_1$ = first term;
$n$ = term number
$r$ = common ratio
The given quadratic sequence has:
$a_{1}=10$ and $r=-1$
Thus, substituting these values into the formula above gives:
$a_{n}=10$$(-1)^{n-1}$
The first five terms are:
$a_{1}=10$
$a_{2}=10$$(-1)^{2-1}$$=-10$
$a_{3}=10$$(-1)^{3-1}$$=10$
$a_{4}=10$$(-1)^{4-1}$$=-10$
$a_{5}=10$$(-1)^{5-1}$$=10$
