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=3), (a_2=6), and (a_n=a_{n-1}+a_{n-2}+2), what is (a_4)?MediumLevel 45What type of sequence is represented by the recursive rule \(a_{n+1}=a_n+7\)?MediumLevel 45If (a_1=2) and (a_{n+1}=a_n+5n-1), what is (a_4)?MediumLevel 45If (a_1=120) and (a_{n+1}=a_n-(3n+2)), what is (a_4)?MediumLevel 45If (a_1=2) and (a_{n+1}=a_n+n^2+n+1), what is (a_4)?MediumLevel 45If (a_1=2) and (a_{n+1}=a_n+n^2+n+1), what is (a_3)?MediumLevel 45If (a_1=16) and (a_{n+1}=a_n+\frac{a_n}{4}), what is (a_3)?MediumLevel 45If a₁ = 4 and aₙ₊₁ = aₙ + 2aₙ, what is a₄?EasyLevel 45If (a_1=1), (a_2=2), and (a_n=3a_{n-1}-2a_{n-2}), what is (a_5)?MediumLevel 45If (a_1=1), (a_2=2), and (a_n=3a_{n-1}-2a_{n-2}), what is (a_4)?MediumLevel 45If (a_1=9) and (a_{n+1}=a_n+2n-2), what is (a_5)?MediumLevel 45If (a_1=9) and (a_{n+1}=a_n+2n-2), what is (a_4)?MediumLevel 45Which of the following sequences is defined by a recursive rule?MediumLevel 45If \(a_1=5\) and \(a_{n+1}=a_n+\frac{n}{2}\), what is \(a_5\)?MediumLevel 45If \(a_1=30\) and \(a_{n+1}=a_n-\frac{n}{2}\), what is \(a_4\)?MediumLevel 45If (a_1=2) and (a_{n+1}=n a_n+1), what is (a_4)?MediumLevel 45If (a_1=5) and (a_{n+1}=a_n+2n+2), what is (a_5)?MediumLevel 46If (a_1=60) and (a_{n+1}=a_n-(3n+1)), what is (a_4)?MediumLevel 46If a₁ = 3 and aₙ₊₁ = 2aₙ + n + 1, what is the value of a₄?MediumLevel 46If a₁ = 7 and aₙ₊₁ = 3aₙ − 2n, what is a₃?MediumLevel 46