Question

A geometric sequence is defined recursively by an = 4an-1. The 1st term of the sequence is 0.5. Which of the following is the explicit formula for the nth term of the sequence? A. 0.5 4n+1 B. 0.5 4n C. 4 0.5n-1 D. 4 0.5n E. 0.5 4n-1

Answer 1

$a_n=4(a_{n-1})$
means the nth term is 4 times the previous term

first term is 0.5
means the next one is 0.5 times 4 or 2
hum, geometric sequence

we can write it as
$a_n=a_1(r)^{n-1}$
where
$a_n$ is the nth term
$a_1$ is the first term
$r$ is the common ratio (what you multiply each term by to get the next term)
$n$ is which term


so first term is 0.5
common ratio is 4
so therfor
$a_n=0.5(4)^{n-1}$
answer is E