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

Question

asked Oct 7, 2020 190k views

2 Answers

Cheshirekow · Answer 1 · 2020-10-12T15:55:15+0000

Answer:

a_n=(2)/(5) a_(n-1)

a_1=500

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

a_n=0.4 a_(n-1)

a_1=500

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 .

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

That is
r=(a_2)/(a_1) or
(a_3)/(a_2) or so on...

r=(200)/(500)=(2)/(5)

So the recursive form for this sequence is:

a_n=(2)/(5) a_(n-1)

a_1=500