Determine whether the given sequence is arithmetic, geometric, or neither. If arithmetic, find the common difference. If
geometric, find the common ratio.
-$\left\{ 3 n ^ { 2 } \right\}$
A) Geometric, $r = 3$
B) Arithmetic, $\mathrm { d } = 3$
C) Neither
D) Geometric, $r = \frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

The given sequence is neither arithmetic nor geometric. In an arithmetic sequence, the difference between consecutive terms is constant, and in a geometric sequence, the ratio of consecutive terms is constant. The sequence $\left\{ 3 n ^ { 2 } \right\}$ represents a quadratic sequence, where each term is three times the square of its position in the sequence, which does not fit the definition of either arithmetic or geometric sequences.

Determine Whether the Given Sequence Is Arithmetic, Geometric, or Neither {3n2}\left\{ 3 n ^ { 2 } \right\}{3n2}

Determine Whether the Given Sequence Is Arithmetic, Geometric, or Neither $\left\{ 3 n ^ { 2 } \right\}$