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

Question

Quizplus · Accepted Answer

The sequence is not arithmetic because the difference between consecutive terms changes. In an arithmetic sequence, the difference between any two consecutive terms is constant, but in this sequence, each term is obtained by multiplying the previous term by $-\frac{1}{6}$, indicating it's a geometric sequence, not arithmetic.

Determine Whether the Sequence Is Arithmetic nnn Begins with 1 an=−(16)na _ { n } = - \left( \frac { 1 } { 6 } \right) ^ { n }an​=−(61​)n

Determine Whether the Sequence Is Arithmetic $n$ Begins with 1 $a _ { n } = - \left( \frac { 1 } { 6 } \right) ^ { n }$