The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-$8,20,32,44,56 , \ldots$
A) $a _ { n } = 8 ( 12 ) ^ { n - 1 }$
B) $a _ { n } = 4 n - 12$
C) $a _ { n } = 12 n - 1$
D) $a _ { n } = 4 ( 3 n - 1 )$

Question

Quizplus · Accepted Answer

The difference between consecutive terms is constant at 12, indicating an arithmetic sequence. The first term is 8, and the common difference is 12. The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference. Substituting $a_1 = 8$ and $d = 12$, we get $a_n = 8 + (n - 1)12 = 12n - 4$, which simplifies to $4(3n - 1)$, matching option D.

The Given Pattern Continues 8,20,32,44,56,…8,20,32,44,56 , \ldots8,20,32,44,56,… A) an=8(12)n−1a _ { n } = 8 ( 12 ) ^ { n - 1 }an​=8(12)n−1

The Given Pattern Continues $8,20,32,44,56 , \ldots$ A) $a _ { n } = 8 ( 12 ) ^ { n - 1 }$