Question

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. an = 38n + 51 , , ,

Answer 1

To find the first four terms of the sequence defined by the formula \( a_n = 38n + 51 \), we will calculate the values for \( n = 1, 2, 3, \) and \( 4 \).

1. For \( n = 1 \):
\[
a_1 = 38(1) + 51 = 38 + 51 = 89
\]

2. For \( n = 2 \):
\[
a_2 = 38(2) + 51 = 76 + 51 = 127
\]

3. For \( n = 3 \):
\[
a_3 = 38(3) + 51 = 114 + 51 = 165
\]

4. For \( n = 4 \):
\[
a_4 = 38(4) + 51 = 152 + 51 = 203
\]

Therefore, the first four terms of the sequence are:
\[
89, 127, 165, 203
\]