Recursive Rule
A recursive rule defines each term of a sequence using one or more previous terms, along with a starting term.
Practice This ConceptMain explanation
Teacher explanation
A recursive rule does not usually give a far-away term directly. It tells how to move from one term to the next. For example, if a1 = 4 and an = an-1 + 3, the sequence is 4, 7, 10, 13, and so on.
Example
If a1 = 2 and each next term is double the previous term, then the sequence is 2, 4, 8, 16.
Simple analogy
Recursive rule says: use the previous term, then move one step.
Common confusion
Students write only the changing rule but forget the starting term, so the sequence cannot be fixed uniquely.
Exam tip
In recursive questions, mention both the first term and the rule for getting the next term.
Study the recursive rule diagram carefully
Use the labelled diagram to keep recursive rule clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of recursive rule in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on recursive rule.
Revision cue
Revise recursive rule through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of recursive rule in one clean line.
2-mark use
Define recursive rule and add one example or condition.
3-mark use
Explain recursive rule, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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