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 = 2(3)n

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Answer 1

To find the first five terms of the sequence defined by \( a_n = 2(3)^n \), we will substitute values of \( n \) starting from 1 to 5.

1. For \( n = 1 \): \[ a_1 = 2(3)^1 = 2 \cdot 3 = 6 \]

2. For \( n = 2 \): \[ a_2 = 2(3)^2 = 2 \cdot 9 = 18 \]

3. For \( n = 3 \): \[ a_3 = 2(3)^3 = 2 \cdot 27 = 54 \]

4. For \( n = 4 \): \[ a_4 = 2(3)^4 = 2 \cdot 81 = 162 \]

5. For \( n = 5 \): \[ a_5 = 2(3)^5 = 2 \cdot 243 = 486 \]

Now, we can list the first five terms of the sequence:

• \( a_1 = 6 \)
• \( a_2 = 18 \)
• \( a_3 = 54 \)
• \( a_4 = 162 \)
• \( a_5 = 486 \)

Thus, the first five terms of the sequence are: \[ 6, 18, 54, 162, 486 \]