What are the first five terms of the recursive sequence?

Question

asked Sep 21, 2023 155k views

1 Answer

Moshood · Answer 1 · 2023-09-27T07:48:58+0000

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.