Answer
Explicit Formula: $a_{n}=1024$$(0.5)^{n-1}$
First five terms: $1024,512,256,128,64$
Work Step by Step
Recall the explicit formula for a geometric sequence:
$a_{n}=$ $a_{1}$ $\times$ $r^{n-1}$
where
$a_n$ = $n^{\text{th}}$ term;
$a_1$ = first term;
$n$ = term number
$r$ = common ratio
The given quadratic sequence has:
$a_{1}=1024$ and $r=0.5$
Thus, substituting these values into the formula above gives:
$a_{n}=1024$$(0.5)^{n-1}$
The first five terms are:
$a_{1}=1024$
$a_{2}=1024$$(0.5)^{2-1}$$=512$
$a_{3}=1024$$(0.5)^{3-1}$$=256$
$a_{4}=1024$$(0.5)^{4-1}$$=128$
$a_{5}=1024$$(0.5)^{5-1}$$=64$
