Find the

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

1 answer

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:

\[ \boxed{223} \]