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

Question

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