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 \(a_1=80\) and \(a_{n+1}=a_n-\frac{n(n+1)}{2}-1\), what is \(a_3\)?MediumLevel 46If \(a_1=14\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_3\)?MediumLevel 46If \(a_1=16\) and \(a_{n+1}=\frac{a_n}{2}+2n\), what is \(a_2\)?MediumLevel 46If (a_1=4) and (a_{n+1}=a_n+3a_1+n), what is (a_3)?MediumLevel 46If (a_1=3), (a_2=4), and (a_n=a_{n-1}+a_{n-2}+2n), what is (a_3)?MediumLevel 46If (a_1=3), (a_2=4), and (a_n=a_{n-1}+a_{n-2}+2n), what is (a_4)?MediumLevel 46If (a_1=4) and (a_{n+1}=a_n^2-2a_n), what is (a_3)?MediumLevel 46Which sequence is defined by a recursive rule?MediumLevel 46If (a_1=3) and (a_{n+1}=a_n^2+a_n+1), what is (a_2)?MediumLevel 46If a₁ = 6 and aₙ₊₁ = aₙ + 4, what is a₉?MediumLevel 46If a₁ = 15 and aₙ₊₁ = aₙ + 8, which term is 71?MediumLevel 46If (a_1=5) and (a_{n+1}=2a_n+3), what is the value of (a_4-a_2)?MediumLevel 46If (a_1=5) and (a_{n+1}=2a_n+3), what is the value of (a_3-a_2)?MediumLevel 46If (a_1=4), (a_2=7), and (a_n=a_{n-1}+a_{n-2}+3), what is (a_5)?MediumLevel 46If (a_1=4), (a_2=7), and (a_n=a_{n-1}+a_{n-2}+3), what is (a_4)?MediumLevel 46For any initial term, which of the following recursive rules generates an arithmetic progression (AP)?MediumLevel 46If (a_1=3) and (a_{n+1}=a_n+6n-1), what is (a_4)?MediumLevel 46If (a_1=3) and (a_{n+1}=a_n+6n-1), what is (a_3)?MediumLevel 46If (a_1=150) and (a_{n+1}=a_n-(4n+3)), what is (a_4)?MediumLevel 46If (a_1=150) and (a_{n+1}=a_n-(4n+3)), what is (a_3)?MediumLevel 46