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 = 4(3)^n
_____, _____, _____, _____

Answer 1

To find the first four terms of the sequence defined by \( a_n = 4(3)^n \), we will substitute values of \( n \) from 1 to 4.

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

2. For \( n = 2 \): \[ a_2 = 4(3)^2 = 4 \times 9 = 36 \]

3. For \( n = 3 \): \[ a_3 = 4(3)^3 = 4 \times 27 = 108 \]

4. For \( n = 4 \): \[ a_4 = 4(3)^4 = 4 \times 81 = 324 \]

Thus, the first four terms of the sequence are: \[ 12, 36, 108, 324 \]

So the answer is: 12, 36, 108, 324