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
upper A subscript n baseline equals 6 plus left parenthesis n minus 1 right parenthesis 1.5

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

An=1.5+(n−1)5.5

Answer 1

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

The first term \( A_1 \) is 1.5.

To find the common difference \( d \), we can subtract the first term from the second term:

\[ d = 7.5 - 1.5 = 6 \]

Now, we can write the explicit formula for an arithmetic sequence:

\[
A_n = A_1 + (n - 1) d
\]

Substituting in the values we have:

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

Thus, the explicit formula for the sequence is:

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

The correct response from your options is:
- \( A_n = 1.5 + (n-1)6 \)