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Question

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.

an = 6n + 2

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Answer 1

To find the first five terms of the sequence defined by \( a_n = 6n + 2 \), we will substitute \( n \) with the values 1 through 5.

1. For \( n = 1 \): \[ a_1 = 6(1) + 2 = 6 + 2 = 8 \]

2. For \( n = 2 \): \[ a_2 = 6(2) + 2 = 12 + 2 = 14 \]

3. For \( n = 3 \): \[ a_3 = 6(3) + 2 = 18 + 2 = 20 \]

4. For \( n = 4 \): \[ a_4 = 6(4) + 2 = 24 + 2 = 26 \]

5. For \( n = 5 \): \[ a_5 = 6(5) + 2 = 30 + 2 = 32 \]

Thus, the first five terms of the sequence are: \[ 8, 14, 20, 26, 32 \]