Answer
Explicit Formula: $a_{n}=$$0.5^{n-1}$
First five terms: $1, 0.5, 0.25, 0.125, 0.0625$
Work Step by Step
Recall the explicit formula for a geometric sequence:
$a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$
where
$a_n$ = $n^{\text{th}}$ term;
$a_1$ = first term;
$n$ = term number'
$r$ = common ratio
The given geometric sequence has:
$a_{1}=1$ and $r=0.5$
Thus, substituing these values into the formula above gives:
$a_{n}=$$0.5^{n-1}$
The first five terms are
:
$a_{1}=1$
$a_{2}=$$0.5^{2-1}$$=0.5$
$a_{3}=$$0.5^{3-1}$$=0.25$
$a_{4}=$$0.5^{4-1}$$=0.125$
$a_{5}=$$0.5^{5-1}$$=0.0625$
