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 = 3n − 1

Answer 1

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

1. For \( n = 1 \): \[ a_1 = 3(1) - 1 = 3 - 1 = 2 \]

2. For \( n = 2 \): \[ a_2 = 3(2) - 1 = 6 - 1 = 5 \]

3. For \( n = 3 \): \[ a_3 = 3(3) - 1 = 9 - 1 = 8 \]

Thus, the first three terms of the sequence are:

• \( a_1 = 2 \)
• \( a_2 = 5 \)
• \( a_3 = 8 \)

So, the first three terms are 2, 5, 8.