Question

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

13th
13th

15th
15th

14th
14th

54 is not a term in the sequence.

Answer 1

To identify which term in the arithmetic sequence \(-18, -12, -6, \ldots\) is equal to 54, we first need to find the common difference and establish a general formula for the terms in the sequence.

1. **Calculate the common difference (d)**:
\[
d = -12 - (-18) = -12 + 18 = 6
\]

2. **Determine the general formula** for the nth term of the arithmetic sequence:
The nth term \(a_n\) can be expressed as:
\[
a_n = a_1 + (n-1) \cdot d
\]
where \(a_1\) is the first term (-18) and \(d\) is the common difference (6).
Therefore:
\[
a_n = -18 + (n-1) \cdot 6
\]
Simplifying this gives:
\[
a_n = -18 + 6n - 6 = 6n - 24
\]

3. **Set the formula equal to 54** to find n:
\[
6n - 24 = 54
\]
Adding 24 to both sides:
\[
6n = 78
\]
Dividing by 6:
\[
n = 13
\]

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

**The answer is: 13th**.