Question

What are the first five terms of the recursive sequence?

Answer 1

Answer: Choice A

9, 30, 93, 282, 849

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Step-by-step explanation:

The first term is 9 because of the notation
`a_1 = 9`

To get the second term, we use the recursive rule given to us which is

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

I recommend using parenthesis to separate things like this

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

If n = 2, then,

`a_n = 3(a_(n-1)) + 3\\\\a_2 = 3(a_(2-1)) + 3\\\\a_2 = 3(a_(1)) + 3\\\\a_2 = 3(9) + 3\\\\a_2 = 27 + 3\\\\a_2 = 30`

The second term is 30.

You can use the same idea as above to find the third term, or you can use this slightly different approach

`\text{third term} = 3*(\text{second term}) + 3\\\\\text{third term} = 3*(30) + 3\\\\\text{third term} = 90 + 3\\\\\text{third term} = 93`

To generate any new term, we first triple the previous term and then add on 3.