Question

What are the first five terms of the recursive sequence

Answer 1

Answer: Choice D

9, 30, 93, 282, 849

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Explanation:

The notation $a_1 = 9$ tells us that the first term is 9

The notation $a_n = 3*(a_{n-1})+3$ says that we multiply the (n-1)st term by 3, then add on 3 to get the nth term $a_n$

So if we wanted the second term for instance, then we'd say

$a_n = 3*(a_{n-1})+3\\\\a_2 = 3*(a_{2-1})+3\\\\a_2 = 3*(a_{1})+3\\\\a_2 = 3*(9)+3\\\\a_2 = 27+3\\\\a_2 = 30$

If we want the third term, then,

$a_n = 3*(a_{n-1})+3\\\\a_3 = 3*(a_{3-1})+3\\\\a_3 = 3*(a_{2})+3\\\\a_3 = 3*(30)+3\\\\a_3 = 90+3\\\\a_3 = 93$

and so on.

The terms so far are: 9, 30, 93

You should find the fourth and fifth terms are 282 and 849 respectively if you keep this pattern going.

Therefore, the answer is choice D