Question

Find the
37th term of a sequence where the first term is 7
and the common difference is 6
.

Answer 1

To find the 37th term of an arithmetic sequence, you can use the formula for the \(n\)-th term of an arithmetic sequence, which is given by:

\[
a_n = a_1 + (n - 1) \cdot d
\]

where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(d\) is the common difference, and
- \(n\) is the term number.

In this case:
- \(a_1 = 7\)
- \(d = 6\)
- \(n = 37\)

Now, plug these values into the formula:

\[
a_{37} = 7 + (37 - 1) \cdot 6
\]

Calculate \(37 - 1\):

\[
37 - 1 = 36
\]

Now multiply by the common difference:

\[
36 \cdot 6 = 216
\]

Now add this to the first term:

\[
a_{37} = 7 + 216 = 223
\]

Thus, the 37th term of the sequence is:

\[
\boxed{223}
\]