Question

Given the explicit formula, an=2(−6)n−1
find the first 5 terms(1 point)
Responses

2, −12, 72, −432, 2592
2, −12, 72, −432, 2592

12, 24, 36, 48, 60
12, 24, 36, 48, 60

−12, −24, −36, −48, −60
−12, −24, −36, −48, −60

12, 72, 432, 2592, 15552

Answer 1

To find the first 5 terms of the sequence defined by the formula \( a_n = 2(-6)^{n-1} \), we can substitute \( n = 1, 2, 3, 4, \) and \( 5 \) into the formula:

1. For \( n = 1 \):
\[
a_1 = 2(-6)^{1-1} = 2(-6)^0 = 2 \times 1 = 2
\]

2. For \( n = 2 \):
\[
a_2 = 2(-6)^{2-1} = 2(-6)^1 = 2 \times -6 = -12
\]

3. For \( n = 3 \):
\[
a_3 = 2(-6)^{3-1} = 2(-6)^2 = 2 \times 36 = 72
\]

4. For \( n = 4 \):
\[
a_4 = 2(-6)^{4-1} = 2(-6)^3 = 2 \times -216 = -432
\]

5. For \( n = 5 \):
\[
a_5 = 2(-6)^{5-1} = 2(-6)^4 = 2 \times 1296 = 2592
\]

So, the first 5 terms are:
\[
2, -12, 72, -432, 2592
\]

Therefore, the correct response is:
\[
\text{2, −12, 72, −432, 2592}
\]