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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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.