Question

Find the 13th term of the arithmetic sequence whose common difference is d=6 and whose first term is a_(1) = 5

Answer 1

In an arithmetic sequence, the \( n \)-th term can be calculated using the formula:

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

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

Given:
- \( a_1 = 5 \)
- \( d = 6 \)
- \( n = 13 \)

We can substitute these values into the formula:

\[
a_{13} = 5 + (13 - 1) \cdot 6
\]

Calculating \( (13 - 1) \):

\[
13 - 1 = 12
\]

Now substitute this value back into the equation:

\[
a_{13} = 5 + 12 \cdot 6
\]

Calculating \( 12 \cdot 6 \):

\[
12 \cdot 6 = 72
\]

Now add this to the first term:

\[
a_{13} = 5 + 72 = 77
\]

Thus, the 13th term of the arithmetic sequence is:

\[
\boxed{77}
\]