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

To determine whether the sequence is arithmetic, we need to check if there is a common difference between any two consecutive terms. 
$$a_2 - a_1 = (6 + 4(2)) - (6 + 4(1)) = 4$$
$$a_3 - a_2 = (6 + 4(3)) - (6 + 4(2)) = 4$$
and so on. 
Since there is a constant difference of 4 between consecutive terms, the sequence is arithmetic with a common difference of $\boxed{\textbf{(D)}\ 4}$.

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 $a _ { n } = 6 + 4 n$