Question

In the arithmetic sequence −18,−12,−6
, . . . , which term is 54?(1 point)
Responses

54 is not a term in the sequence.
54 is not a term in the sequence.

15th
15th

13th
13th

14th

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.

For the given sequence \(-18, -12, -6, \ldots\):
- The first term \( a_1 = -18 \)
- The common difference \( d = -12 - (-18) = 6 \)

We want to find \( n \) such that:

\[
a_n = 54
\]

Plugging the values into the formula:

\[
54 = -18 + (n - 1) \cdot 6
\]

Now, solve for \( n \):

\[
54 + 18 = (n - 1) \cdot 6
\]

\[
72 = (n - 1) \cdot 6
\]

Now, divide by 6:

\[
n - 1 = \frac{72}{6}
\]

\[
n - 1 = 12
\]

Adding 1 to both sides:

\[
n = 13
\]

Thus, the 13th term of the sequence is 54.

The correct response is:

**13th**