Question

the general form for the nth term of a sequence is $a_{n} = a_{1} cdot r^{n - 1}$

Explanation:

Step1: Recall Sequence Types

We know different sequences: arithmetic (common difference) and geometric (common ratio). The formula \(a_n = a_1 \cdot r^{n - 1}\) has a common ratio \(r\) (multiplication of \(r\) for each term).

Step2: Identify Sequence Type

Arithmetic sequence formula is \(a_n=a_1+(n - 1)d\) (with difference \(d\)). Geometric sequence has terms multiplied by \(r\), so the formula \(a_n = a_1 \cdot r^{n - 1}\) is for a geometric sequence.

Answer:

geometric