Question

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

Answer 1

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 \( 14 - 1 \):

\[
14 - 1 = 13
\]

2. Multiply by the common difference:

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

3. Add this result to the first term:

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

Thus, the 14th term of the sequence is

\[
\boxed{-34}
\]