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 = 4(3)n

Answer 1

To find the first five terms of the sequence defined by \( a_n = 4(3)^n \), we will substitute \( n = 1, 2, 3, 4, 5 \) into the formula.

1. For \( n = 1 \):
\[
a_1 = 4(3)^1 = 4 \times 3 = 12
\]

2. For \( n = 2 \):
\[
a_2 = 4(3)^2 = 4 \times 9 = 36
\]

3. For \( n = 3 \):
\[
a_3 = 4(3)^3 = 4 \times 27 = 108
\]

4. For \( n = 4 \):
\[
a_4 = 4(3)^4 = 4 \times 81 = 324
\]

5. For \( n = 5 \):
\[
a_5 = 4(3)^5 = 4 \times 243 = 972
\]

Thus, the first five terms of the sequence are:

- \( a_1 = 12 \)
- \( a_2 = 36 \)
- \( a_3 = 108 \)
- \( a_4 = 324 \)
- \( a_5 = 972 \)

In summary, the first five terms are \( 12, 36, 108, 324, 972 \).