alleryStart learning →What two parts must every recursive formula supply?
AAn initial term and an equation using earlier terms
BAn initial term and a fixed common difference value
CA general term and a fixed upper limit of summation
DA general term and an equation using the index only
Answer & Solution
Correct answer: A. An initial term and an equation using earlier terms
1. A recursive rule builds each term out of terms already known, so it needs somewhere to start.
2. The first part is therefore the value of an initial term, or of two initial terms when the rule reaches back that far.
3. The second part is an equation defining the general term using one or more preceding terms.
4. A rule written purely in terms of the index n is an explicit formula, not a recursive one, which rules out the last option.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 Sequences and Their Notations_
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