Answer
Explicit Formula: $a_{n}=100$$(-20)^{n-1}$
First five terms: $100,-2000,40000,-800000,16000000$
Work Step by Step
Recall the explicit formula for a geometric sequence:
$a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$
where
$a_n$ = $n^{\text{th}}$ term;
$a_1$ = first term;
$n$ = term number'
$r$ = common ratio
The given geometric sequence has:
$a_{1}=100$ and $r=-20$
Thus, subsituting these values into the formula above gives:
$a_{n}=100$$(-20)^{n-1}$
The first five terms are:
$a_{1}=100$
$a_{2}=100$$(-20)^{2-1}$$=-2000$
$a_{3}=100$$(-20)^{3-1}$$=40000$
$a_{4}=100$$(-20)^{4-1}$$=-800000$
$a_{5}=100$$(-20)^{5-1}$$=16000000$
