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.

Question

an = 4(2)n

,
,
,
,

Answer 1

The sequence defined by the formula \( a_n = 4(2)^n \) can be evaluated for the first five terms by substituting \( n = 1, 2, 3, 4, \) and \( 5 \).

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

Thus, the first five terms of the sequence are: \[ 8, 16, 32, 64, 128 \]