The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
-$$a _ { n } = 3 n ^ { 2 } - 4$$
A) arithmetic, $\mathrm { d } = - 4$
B) geometric, $r = 3$
C) arithmetic, $d = 3$
D) neither

Question

Quizplus · Accepted Answer

The given sequence $a_n = 3n^2 - 4$ is neither arithmetic nor geometric because the difference between consecutive terms changes as $n$ increases, and the ratio between consecutive terms also changes. Arithmetic sequences have a constant difference between terms, and geometric sequences have a constant ratio between terms, neither of which applies here.

The General Term of a Sequence Is Given an=3n2−4a _ { n } = 3 n ^ { 2 } - 4an​=3n2−4

The General Term of a Sequence Is Given $a _ { n } = 3 n ^ { 2 } - 4$