Question

of the sequence based on their equations
5.) $a_n = 15 - 6(n - 1)$ \t 6.) $a_n = n^2 + 6n$
___, _, _, _, _ \t _, _, _, _, ___

Explanation:

Step1: Analyze Sequence 5 ($a_n = 15 - 6(n - 1)$)

First, simplify the formula: $a_n = 15 - 6n + 6 = 21 - 6n$.
For $n = 1$: $a_1 = 21 - 6(1) = 15$.
For $n = 2$: $a_2 = 21 - 6(2) = 9$.
For $n = 3$: $a_3 = 21 - 6(3) = 3$.
For $n = 4$: $a_4 = 21 - 6(4) = -3$.
For $n = 5$: $a_5 = 21 - 6(5) = -9$.

Step2: Analyze Sequence 6 ($a_n = n^2 + 6n$)

For $n = 1$: $a_1 = 1^2 + 6(1) = 7$.
For $n = 2$: $a_2 = 2^2 + 6(2) = 4 + 12 = 16$.
For $n = 3$: $a_3 = 3^2 + 6(3) = 9 + 18 = 27$.
For $n = 4$: $a_4 = 4^2 + 6(4) = 16 + 24 = 40$.
For $n = 5$: $a_5 = 5^2 + 6(5) = 25 + 30 = 55$.

Answer:

For $a_n = 15 - 6(n - 1)$: $15, 9, 3, -3, -9$
For $a_n = n^2 + 6n$: $7, 16, 27, 40, 55$