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

Question

an = 25n + 31

Answer 1

To find the first four terms of the sequence defined by the formula \( a_n = 25n + 31 \), we will substitute the values of \( n \) from 1 to 4 into the formula.

1. For \( n = 1 \): \[ a_1 = 25(1) + 31 = 25 + 31 = 56 \]

2. For \( n = 2 \): \[ a_2 = 25(2) + 31 = 50 + 31 = 81 \]

3. For \( n = 3 \): \[ a_3 = 25(3) + 31 = 75 + 31 = 106 \]

4. For \( n = 4 \): \[ a_4 = 25(4) + 31 = 100 + 31 = 131 \]

Thus, the first four terms of the sequence are:

• \( a_1 = 56 \)
• \( a_2 = 81 \)
• \( a_3 = 106 \)
• \( a_4 = 131 \)

The final result is: \[ 56, 81, 106, 131 \]