Question

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

an = 2(4)^n

Answer 1

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

1. For \( n = 1 \):
\[
a_1 = 2(4^1) = 2(4) = 8
\]

2. For \( n = 2 \):
\[
a_2 = 2(4^2) = 2(16) = 32
\]

3. For \( n = 3 \):
\[
a_3 = 2(4^3) = 2(64) = 128
\]

Thus, the first three terms of the sequence are:
- \( a_1 = 8 \)
- \( a_2 = 32 \)
- \( a_3 = 128 \)

So the terms are \( 8, 32, 128 \).