Use the Formula for the General Term of a Geometric SequenceUse the formula for the general term (the nth term)of a geometric sequence to find the indicated term of the
sequence with the given first term, $$\mathbf { a } _ { 1 }$$ , and common ratio, r.
-$$a _ { n } = 4 n ^ { 2 } - 3$$
A) arithmetic, $d = - 3$
B) geometric, $r = 4$
C) arithmetic, $d = 4$
D) neither

Question

Quizplus · Accepted Answer

The given formula $a_n = 4n^2 - 3$ does not represent a geometric sequence because the nth term does not take the form of $a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term and $r$ is the common ratio. Instead, it represents a quadratic sequence, which is neither arithmetic (where each term is obtained by adding a constant difference to the previous term) nor geometric (where each term is obtained by multiplying the previous term by a constant ratio).

Use the Formula for the General Term of a Geometric a1\mathbf { a } _ { 1 }a1​

Use the Formula for the General Term of a Geometric $\mathbf { a } _ { 1 }$