Question

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 = 2n − 7

Answer 1

To find the first three terms of the sequence defined by the formula \( a_n = 2n - 7 \), we will substitute \( n \) with \( 1 \), \( 2 \), and \( 3 \).

1. For \( n = 1 \):
\[
a_1 = 2(1) - 7 = 2 - 7 = -5
\]

2. For \( n = 2 \):
\[
a_2 = 2(2) - 7 = 4 - 7 = -3
\]

3. For \( n = 3 \):
\[
a_3 = 2(3) - 7 = 6 - 7 = -1
\]

Thus, the first three terms of the sequence are:

- \( a_1 = -5 \)
- \( a_2 = -3 \)
- \( a_3 = -1 \)

In summary, the first three terms of the sequence are: \(-5, -3, -1\).