Question

6 which of these is a formula that can be used to determine the nth term of the arithmetic sequence 15, 27, 39, 51,...? a ( a_n = 12n + 3 ) b ( a_n = 15n + 12 ) c ( a_n = 12n + 15 ) d ( a_n = 3n + 12 )

Explanation:

Step1: Find first term \(a_1\)

First term \(a_1 = 15\)

Step2: Calculate common difference \(d\)

\(d = 27 - 15 = 12\)

Step3: Use arithmetic sequence formula

\(a_n = a_1 + (n-1)d = 15 + (n-1)×12 = 12n + 3\)

Step4: Verify with \(n=1\)

\(12×1 + 3 = 15\) (matches first term)

Step5: Verify with \(n=2\)

\(12×2 + 3 = 27\) (matches second term)

Answer:

A. \(a_n = 12n + 3\)