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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 = 3n − 7

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To find the first five terms of the sequence defined by the formula \( a_n = 3n - 7 \), we will evaluate the formula for \( n = 1, 2, 3, 4, \) and \( 5 \).

  1. For \( n = 1 \): \[ a_1 = 3(1) - 7 = 3 - 7 = -4 \]

  2. For \( n = 2 \): \[ a_2 = 3(2) - 7 = 6 - 7 = -1 \]

  3. For \( n = 3 \): \[ a_3 = 3(3) - 7 = 9 - 7 = 2 \]

  4. For \( n = 4 \): \[ a_4 = 3(4) - 7 = 12 - 7 = 5 \]

  5. For \( n = 5 \): \[ a_5 = 3(5) - 7 = 15 - 7 = 8 \]

Thus, the first five terms of the sequence are: \[ -4, -1, 2, 5, 8 \]