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

1 answer

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:

\[ \boxed{77} \]