Question

What is the explicit formula for the arithmetic sequence 1.5, 7.5, 13.5, 19.5, 25.5, . . . ?(1 point)
Responses

An=1.5+(n−1)6
𝐴
𝑛
=
1.5
+
(
𝑛
−
1
)
6
upper A subscript n baseline equals 1.5 plus left parenthesis n minus 1 right parenthesis 6

An=6+(n−1)1.5
𝐴
𝑛
=
6
+
(
𝑛
−
1
)
1.5
upper A subscript n baseline equals 6 plus left parenthesis n minus 1 right parenthesis 1.5

An=5.5+(n−1)1.5
𝐴
𝑛
=
5.5
+
(
𝑛
−
1
)
1.5
upper A subscript n baseline equals 5.5 plus left parenthesis n minus 1 right parenthesis 1.5

An=1.5+(n−1)5.5

Answer 1

To find the explicit formula for the arithmetic sequence \(1.5, 7.5, 13.5, 19.5, 25.5, \ldots\), we need to determine the first term and the common difference.

1. The first term \(A_1\) is \(1.5\).
2. The common difference \(d\) can be calculated from the difference between consecutive terms:
\[
d = 7.5 - 1.5 = 6
\]

Now, the general formula for an arithmetic sequence can be expressed as:
\[
A_n = A_1 + (n - 1)d
\]

Substituting the identified values:
\[
A_n = 1.5 + (n - 1) \cdot 6
\]

Thus, the explicit formula for this arithmetic sequence is:
\[
A_n = 1.5 + (n - 1) \cdot 6
\]

So the correct answer is:
**\(A_n = 1.5 + (n - 1) \cdot 6\)**.