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.

Question

an = 3(4)n

Answer 1

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

1. For \( n = 1 \): \[ a_1 = 3(4)^1 = 3 \times 4 = 12 \]

2. For \( n = 2 \): \[ a_2 = 3(4)^2 = 3 \times 16 = 48 \]

3. For \( n = 3 \): \[ a_3 = 3(4)^3 = 3 \times 64 = 192 \]

Thus, the first three terms of the sequence are:

• \( a_1 = 12 \)
• \( a_2 = 48 \)
• \( a_3 = 192 \)

The first three terms of the sequence are \( 12, 48, 192 \).