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.

Question

an = 3(4)n

Answer 1

To find the first four terms of the sequence defined by the formula \( a_n = 3(4^n) \), we can calculate the values for \( n = 1, 2, 3, \) and \( 4 \).

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

4. For \( n = 4 \): \[ a_4 = 3(4^4) = 3 \times 256 = 768 \]

Thus, the first four terms of the sequence are:

• \( a_1 = 12 \)
• \( a_2 = 48 \)
• \( a_3 = 192 \)
• \( a_4 = 768 \)

In summary, the first four terms are 12, 48, 192, 768.