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Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = 3n − 6

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To find the first three terms of the sequence defined by the formula \( a_n = 3n - 6 \), we will substitute \( n = 1 \), \( n = 2 \), and \( n = 3 \) into the formula.

  1. For \( n = 1 \): \[ a_1 = 3(1) - 6 = 3 - 6 = -3 \]

  2. For \( n = 2 \): \[ a_2 = 3(2) - 6 = 6 - 6 = 0 \]

  3. For \( n = 3 \): \[ a_3 = 3(3) - 6 = 9 - 6 = 3 \]

Thus, the first three terms of the sequence are:

  • \( a_1 = -3 \)
  • \( a_2 = 0 \)
  • \( a_3 = 3 \)

Final Answer:

  • The first three terms of the sequence are \(-3, 0, 3\).