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1 vote
The recursive rule for a geometric sequence is given. a1=2;an=13an−1

2 Answers

2 votes

Answer:

The answer would actually be:
2((1)/(3))^(n-1)

Explanation:

I just took the test.

7 votes
The complete question is:
The recursive rule for a geometric sequence is given.
a_(1)=2;
a_(n)= 13*a_(n-1). Enter the explicit rule for the sequence.

Solution:
We are given

a_(1)=2 \\ \\ a_(n) = a_(n-1)

Explicit rule of geometric sequence is of the form:


a_(n) = a_(1) (r)^(n-1)

Using the given recursive sequence, we can find r.


a_(1)=2

a_(2)=13* a_(1)=13*2=26

r = Ratio of consecutive two terms of Geometric series.
So,
r = 26/2 = 13

Therefore,


a_(n)=2(13)^(n-1) is the explicit rule for the given geometric sequence.

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