Question

Complete the recursive formula of the geometric sequence {500, 200, 80, 32}​

Answer 1

Answer:

$a_n=\frac{2}{5} a_{n-1}$

$a_1=500$

----------------------or one might prefer the answer so that $r$ is a decimal:

$a_n=0.4 a_{n-1}$

$a_1=500$

Step-by-step explanation:

The recursive form got a geometric sequence is $a_n=r \cdot a_{n-1}$ with a term given such as the first term, $a_1$.

$r$ can be determined by choosing a term from the sequence and dividing by it's previous term.

That is $r=\frac{a_2}{a_1}$ or $\frac{a_3}{a_2}$ or so on...

$r=\frac{200}{500}=\frac{2}{5}$

So the recursive form for this sequence is:

$a_n=\frac{2}{5} a_{n-1}$

$a_1=500$