Question

select the correct choice that completes the sentence. an arithmetic sequence can always be expressed as a(n) sequence. increasing recursive fibonacci alternating

Explanation:

An arithmetic sequence has a common difference \(d\). The recursive formula for an arithmetic sequence is \(a(n)=a(n - 1)+d\), where \(a(1)\) is the first - term.

• An increasing sequence is not always the case for an arithmetic sequence. If \(d>0\), it is increasing; if \(d = 0\), it is a constant sequence; if \(d<0\), it is decreasing.
• A Fibonacci - type sequence is defined by \(a(n)=a(n - 1)+a(n - 2)\) (\(n\geq3\)), which is different from the rule of an arithmetic sequence.
• An alternating sequence has terms that alternate in sign (e.g., \(a, - a,a, - a,\cdots\)) which is not related to the general form of an arithmetic sequence \(a(n)=a(1)+(n - 1)d\).

Answer:

recursive