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 = –7n + 1 , ,

Answer 1

To find the first three terms of the sequence defined by \( a_n = -7n + 1 \), we will calculate \( a_1 \), \( a_2 \), and \( a_3 \).

1. For \( n = 1 \):
\[
a_1 = -7(1) + 1 = -7 + 1 = -6
\]

2. For \( n = 2 \):
\[
a_2 = -7(2) + 1 = -14 + 1 = -13
\]

3. For \( n = 3 \):
\[
a_3 = -7(3) + 1 = -21 + 1 = -20
\]

Thus, the first three terms of the sequence are:
- \( a_1 = -6 \)
- \( a_2 = -13 \)
- \( a_3 = -20 \)

In summary, the first three terms are \(-6\), \(-13\), and \(-20\).