Question

what is the explicit formula for the arithmetic sequence 1.5, 7.5, 13.5, 19.5, 25.5, ... ? (1 point) \\( a_n = 1.5 + (n - 1) 6 \\) \\( a_n = 1.5 + (n - 1) 5.5 \\) \\( a_n = 5.5 + (n - 1) 1.5 \\) \\( a_n = 6 + (n - 1) 1.5 \\)

Explanation:

Step1: Recall Arithmetic Sequence Formula

The explicit formula for an arithmetic sequence is \( A_n = a_1 + (n - 1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.

Step2: Identify \( a_1 \)

In the sequence \( 1.5, 7.5, 13.5, 19.5, 25.5, \dots \), the first term \( a_1 = 1.5 \).

Step3: Calculate Common Difference \( d \)

Subtract consecutive terms: \( 7.5 - 1.5 = 6 \), \( 13.5 - 7.5 = 6 \), etc. So \( d = 6 \).

Step4: Substitute into Formula

Substitute \( a_1 = 1.5 \) and \( d = 6 \) into \( A_n = a_1 + (n - 1)d \), we get \( A_n = 1.5 + (n - 1)6 \).

Answer:

A. \( A_n = 1.5 + (n - 1)6 \)