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

We can use the formula for the nth term of an arithmetic sequence to check if it matches the given sequence: 
$$a_n = a_1 + (n-1)d$$
Substituting in the given values, we get: 
$$-6 + 4n = -6 + (n-1)d$$
Simplifying, we get: 
$$4n = (n-1)d$$
Therefore, the sequence is arithmetic with a common difference of d = 4, which means the answer is choice 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 $a _ { n } = - 6 + 4 n$