Question

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

An=6+(n−1)1.5
cap A sub n is equal to 6 plus open paren n minus 1 close paren times 1 point 5

An=1.5+(n−1)6
cap A sub n is equal to 1 point 5 plus open paren n minus 1 close paren times 6

An=5.5+(n−1)1.5
cap A sub n is equal to 5 point 5 plus open paren n minus 1 close paren times 1 point 5

An=1.5+(n−1)5.5

Answer 1

To find the explicit formula for the arithmetic sequence given, we need to identify the first term and the common difference.

1. **First term \(a_1\)**: The first term is \(1.5\).
2. **Common difference \(d\)**: The difference between consecutive terms:
- \(7.5 - 1.5 = 6\)
- \(13.5 - 7.5 = 6\)
- \(19.5 - 13.5 = 6\)
- \(25.5 - 19.5 = 6\)

Thus, the common difference \(d = 6\).

The explicit formula for the \(n\)-th term of an arithmetic sequence can be written as:

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

Substituting the values we found:

\[
A_n = 1.5 + (n-1) \cdot 6
\]

So the correct formula is:

\[
A_n = 1.5 + (n-1)6
\]

Thus, the answer is:

**An=1.5+(n−1)6**