Question

A recursive rule for a geometric sequence is a1=49;an=3an−1. What is the explicit rule for this sequence?

Answer 1

(4/9)(3)^n-1

explanation:

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Answer 2

`a_n = 49(3)^(n-1)`

Explanation:

A recursive rule for a geometric sequence is a1=49;an=3an−1

First term a1= 49

`a_n=3*a_(n-1)`

`a_2=3*a_(1)`

`a_2=3*49}`

To get second term, multiply the first term by 3

So common ratio r = 3

Explicit rule for geometric sequence is

`a_n = a_1(r)^(n-1)`

a1= 49 and r= 3

So explicit rule is

`a_n = 49(3)^(n-1)`