Question

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

Answer 1

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

Explanation:

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Answer 2

Explicit rule is

`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_2= 3 * a_1= 3*49= 147`

`a_2= 3 * a_2= 3*147= 441`

To get second term, multiply the first term by 3

So common ratio = 3

Explicit rule for geometric sequence is

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

Where a1 is the first term

r is the common ratio

a1= 49 and r= 3

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