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

User Conrad
by
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2 Answers

7 votes

Answer:(2/5)An-1

Explanation:

2 votes

Answer:


a_n=(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

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=(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

User Cheshirekow
by
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