Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that $n$ begins with 1.)
$$a _ { n } = - 6 + 4 n$$
A) $- 4$
B) 6
C) $- 6$
D) 4
E) not arithmetic

Question

Quizplus · Accepted Answer

The sequence is arithmetic if there is a common difference between each term. 
We can check if there is a constant difference by subtracting two consecutive terms: 
$$(a_{n+1} - a_n) = (-6 + 4(n+1)) - (-6 + 4n) = 4$$
Since the difference is a constant value of 4, the sequence is arithmetic with a common difference of 4. Therefore, the answer is (D).

Determine Whether the Sequence Is Arithmetic nnn Begins with 1 an=−6+4na _ { n } = - 6 + 4 nan​=−6+4n

Determine Whether the Sequence Is Arithmetic $n$ Begins with 1 $a _ { n } = - 6 + 4 n$