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=5) and (a_{n+1}=2a_n-2n), what is (a_3)?MediumLevel 44If (a_1=1), (a_2=4), and (a_n=a_{n-1}+2a_{n-2}), what is (a_5)?MediumLevel 44If (a_1=2), (a_2=5), and (a_n=2a_{n-1}-a_{n-2}), what is (a_6)?MediumLevel 44If (a_1=3) and (a_{n+1}=a_n+n^2), what is (a_5)?MediumLevel 44If (a_1=3) and (a_{n+1}=a_n+n^2), what is (a_4)?MediumLevel 44If (a_1=50) and (a_{n+1}=a_n-(2n+3)), what is (a_4)?MediumLevel 44If (a_1=2) and (a_{n+1}=3a_n+1), what is (a_4)?MediumLevel 44If (a_1=2) and (a_{n+1}=3a_n+1), what is (a_3)?MediumLevel 44If \(a_1=10\) and \(a_{n+1}=\frac{a_n}{2}+n\), what is \(a_4\)?MediumLevel 44If \(a_1=10\) and \(a_{n+1}=\frac{a_n}{2}+n\), what is \(a_3\)?MediumLevel 44If (a_1=1), (a_2=3), and (a_n=2a_{n-1}+a_{n-2}), what is (a_5)?MediumLevel 44If (a_1=1), (a_2=3), and (a_n=2a_{n-1}+a_{n-2}), what is (a_4)?MediumLevel 44If (a_1=4) and (a_{n+1}=a_n+3n-1), what is (a_5)?MediumLevel 44If (a_1=4) and (a_{n+1}=a_n+3n-1), what is (a_4)?MediumLevel 44If (a_1=2) and (a_{n+1}=a_n^2-1), what is (a_3)?MediumLevel 44If (a_1=6) and (a_{n+1}=a_n+n+2), what is the value of (a_5)?MediumLevel 44If (a_1=7) and (a_{n+1}=a_n+4n+1), what is (a_4)?MediumLevel 44If \(a_1=80\) and \(a_{n+1}=\frac{a_n}{2}-n\), what is \(a_3\)?MediumLevel 44If a₁ = 84 and aₙ₊₁ = aₙ/2 − n, what is a₃?MediumLevel 44If \(a_1=88\) and \(a_{n+1}=\frac{a_n}{2}-n\), what is \(a_2\)?MediumLevel 44