Question

Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = 2(3)n

,
,
,
,

Answer 1

To find the first five terms of the sequence defined by \( a_n = 2(3)^n \), we will substitute values of \( n \) starting from 1 to 5.

1. For \( n = 1 \):
\[
a_1 = 2(3)^1 = 2 \cdot 3 = 6
\]

2. For \( n = 2 \):
\[
a_2 = 2(3)^2 = 2 \cdot 9 = 18
\]

3. For \( n = 3 \):
\[
a_3 = 2(3)^3 = 2 \cdot 27 = 54
\]

4. For \( n = 4 \):
\[
a_4 = 2(3)^4 = 2 \cdot 81 = 162
\]

5. For \( n = 5 \):
\[
a_5 = 2(3)^5 = 2 \cdot 243 = 486
\]

Now, we can list the first five terms of the sequence:
- \( a_1 = 6 \)
- \( a_2 = 18 \)
- \( a_3 = 54 \)
- \( a_4 = 162 \)
- \( a_5 = 486 \)

Thus, the first five terms of the sequence are:
\[
6, 18, 54, 162, 486
\]