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 = 6(8)^n

Answer 1

To find the first five terms of the sequence defined by \( a_n = 6(8)^n \), we will substitute \( n \) with the values 1 through 5.

1. For \( n = 1 \):
\[
a_1 = 6(8)^1 = 6 \times 8 = 48
\]

2. For \( n = 2 \):
\[
a_2 = 6(8)^2 = 6 \times 64 = 384
\]

3. For \( n = 3 \):
\[
a_3 = 6(8)^3 = 6 \times 512 = 3072
\]

4. For \( n = 4 \):
\[
a_4 = 6(8)^4 = 6 \times 4096 = 24576
\]

5. For \( n = 5 \):
\[
a_5 = 6(8)^5 = 6 \times 32768 = 196608
\]

Thus, the first five terms of the sequence are:
1. \( a_1 = 48 \)
2. \( a_2 = 384 \)
3. \( a_3 = 3072 \)
4. \( a_4 = 24576 \)
5. \( a_5 = 196608 \)

So, the final answer is:
\[
\{ 48, 384, 3072, 24576, 196608 \}
\]