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)5.5
cap A sub n is equal to 1 point 5 plus open paren n minus 1 close paren times 5 point 5 - no response given

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 - incorrect

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 - no response given

An=1.5+(n−1)6

Answer 1

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

1. The first term \( a_1 \) of the sequence is \( 1.5 \).
2. To find the common difference \( d \), we can calculate the difference between the second term and the first term:
\[
d = 7.5 - 1.5 = 6
\]

Now that we have the first term and the common difference, we can use the formula for the \( n \)-th term of an arithmetic sequence, which is given by:

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

Plugging in the values:
- \( a_1 = 1.5 \)
- \( d = 6 \)

The formula becomes:

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

Thus, the explicit formula for the arithmetic sequence is:

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

From your options, the correct response is:

**An = 1.5 + (n - 1)6**