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.

Question

an = –65n + 12

Answer 1

To find the first three terms of the sequence defined by the formula \( a_n = -65n + 12 \), we will substitute \( n = 1 \), \( n = 2 \), and \( n = 3 \) into the formula.

1. For \( n = 1 \): \[ a_1 = -65(1) + 12 = -65 + 12 = -53 \]

2. For \( n = 2 \): \[ a_2 = -65(2) + 12 = -130 + 12 = -118 \]

3. For \( n = 3 \): \[ a_3 = -65(3) + 12 = -195 + 12 = -183 \]

Thus, the first three terms of the sequence are: \[ -53, -118, -183 \]