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(2)n , , , , Submit

Answer 1

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

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

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

3. For \( n = 3 \):
\[
a_3 = 4(2)^3 = 4 \times 8 = 32
\]

4. For \( n = 4 \):
\[
a_4 = 4(2)^4 = 4 \times 16 = 64
\]

5. For \( n = 5 \):
\[
a_5 = 4(2)^5 = 4 \times 32 = 128
\]

Therefore, the first five terms of the sequence are:
- \( a_1 = 8 \)
- \( a_2 = 16 \)
- \( a_3 = 32 \)
- \( a_4 = 64 \)
- \( a_5 = 128 \)

The first five terms of the sequence are: **8, 16, 32, 64, 128**.