Mathematics
Recursive rule
पुनरावर्ती नियम
In Class 9 Mathematics, the topic Recursive Rule in Sequences and Progressions explains how a sequence can be defined by giving one or more starting terms and a rule that uses earlier terms to find the next one. Students learn to read and write such rules, generate sequence terms step by step, recognize patterns, and check whether a rule correctly describes a sequence. The topic also connects recursive descriptions with familiar arithmetic and geometric progressions, helping students understand how terms change and how sequence patterns can be represented mathematically.
Practice questions
If (a_1=2) and (a_{n+1}=a_n+n(n+2)), what is (a_3)?MediumLevel 45If (a_1=100) and (a_{n+1}=a_n-n(n+2)), what is (a_4)?MediumLevel 45If (a_1=7) and (a_{n+1}=2a_n+3), what is (a_4)?MediumLevel 45If (a_1=7) and (a_{n+1}=2a_n+3), what is (a_3)?MediumLevel 45Which recursive rule produces an arithmetic progression with common difference 5 for any initial term \(a_1\)?MediumLevel 45Which additional information is necessary to determine a sequence uniquely from the recursive rule \(a_{n+1}=2a_n+5\)?MediumLevel 45If \(a_1=3\) and \(a_{n+1}=a_n+\frac{n(n+1)}{2}\), what is \(a_5\)?MediumLevel 45If \(a_1=70\) and \(a_{n+1}=a_n-\frac{n(n+1)}{2}\), what is \(a_4\)?MediumLevel 45If \(a_1=10\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_3\)?MediumLevel 45If \(a_1=12\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_2\)?MediumLevel 45If (a_1=6) and (a_{n+1}=a_n+2a_1+n), what is (a_3)?MediumLevel 45If a sequence is defined by the recursive rule \(a_{n+1}=a_n+5\), what type of sequence is it?MediumLevel 45If (a_1=2), (a_2=4), and (a_n=a_{n-1}+a_{n-2}+n), what is (a_4)?MediumLevel 45If (a_1=2), (a_2=4), and (a_n=a_{n-1}+a_{n-2}+n), what is (a_3)?MediumLevel 45If (a_1=3) and (a_{n+1}=a_n^2-a_n), what is (a_3)?MediumLevel 45If (a_1=2) and (a_{n+1}=a_n^2+a_n), what is (a_3)?MediumLevel 45If (a_1=4) and (a_{n+1}=a_n+3), what is (a_8)?MediumLevel 45If (a_1=9) and (a_{n+1}=a_n+7), which term is (51)?MediumLevel 45If (a_1=4) and (a_{n+1}=2a_n+1), what is the value of (a_4-a_2)?MediumLevel 45If (a_1=3), (a_2=6), and (a_n=a_{n-1}+a_{n-2}+2), what is (a_5)?MediumLevel 45