Question

Find the first four 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 , , , Submit

Answer 1

To find the first four terms of the sequence defined by \( a_n = 6(8^n) \), we will substitute \( n \) with values from 1 to 4.

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

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

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

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

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

So the first four terms are: \( 48, 384, 3072, 24576 \).