Find the

14th term of a sequence where the first term is -8
and the common difference is -2
.

1 answer

To find the 14th term of an arithmetic sequence, you can use the formula for the nth term of an arithmetic sequence, which is given by:

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

where:

  • \( a_n \) is the nth term,
  • \( a_1 \) is the first term,
  • \( d \) is the common difference, and
  • \( n \) is the term number.

In this case, we have:

  • \( a_1 = -8 \)
  • \( d = -2 \)
  • \( n = 14 \)

Now, substituting the values into the formula:

\[ a_{14} = -8 + (14 - 1) \cdot (-2) \]

Calculating the expression step by step:

  1. Calculate \( 14 - 1 \):

\[ 14 - 1 = 13 \]

  1. Multiply by the common difference:

\[ 13 \cdot (-2) = -26 \]

  1. Add this result to the first term:

\[ a_{14} = -8 + (-26) = -8 - 26 = -34 \]

Thus, the 14th term of the sequence is

\[ \boxed{-34} \]