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 a₁ = 7 and aₙ₊₁ = 2aₙ + (−1)ⁿn, what is a₅?HardLevel 44If (a_1=6) and (a_{n+1}=a_n+2^n+n^2), what is (a_5)?ExpertLevel 44If a₁ = 200 and aₙ₊₁ = aₙ − (3ⁿ + n), what is a₄?HardLevel 44If (a_1=5) and (a_{n+1}=a_n+n!+n), what is (a_5)?ExpertLevel 44If (a_1=90) and (a_{n+1}=a_n-(n!+2n)), what is (a_5)?ExpertLevel 44If (a_1=3) and (a_{n+1}=4a_n-(n+1)), what is (a_3)?ExpertLevel 44If (a_1=2), (a_2=6), and (a_n=a_{n-1}+2a_{n-2}+n^2), what is (a_4)?ExpertLevel 44If a₁ = 5, a₂ = 11, and aₙ = 3aₙ₋₁ − 2aₙ₋₂, what is a₅?HardLevel 44If (a_1=8) and (a_{n+1}=a_n+n(n+2)+2^n), what is (a_4)?ExpertLevel 44If a₁ = 180 and aₙ₊₁ = aₙ − (n(n + 2) + 2ⁿ), what is a₄?HardLevel 44If (a_1=9) and (a_{n+1}=2a_n+3n-2), what is (a_3)?ExpertLevel 44If \(a_1=30\) and \(a_{n+1}=\frac{a_n}{3}+2n^2\), what is \(a_3\)?ExpertLevel 44If (a_1=5) and (a_{n+1}=a_n+3a_1+n^2), what is (a_3)?ExpertLevel 44If a₁ = 2, a₂ = 4, and aₙ = aₙ₋₁ + aₙ₋₂ + 3n, what is a₅?HardLevel 44If (a_1=2), (a_2=5), and (a_n=2a_{n-1}+a_{n-2}+n^2), what is (a_4)?ExpertLevel 44If (a_1=3) and (a_{n+1}=a_n^2-2a_n+4), what is (a_3)?ExpertLevel 44If (a_1=4) and (a_{n+1}=a_n^2-a_n+2), what is (a_2)?ExpertLevel 44If (a_1=13) and (a_{n+1}=a_n+6), which term is (79)?ExpertLevel 44If (a_1=8) and (a_{n+1}=a_n+9), what is (a_{12})?ExpertLevel 44If (a_1=4) and (a_{n+1}=2a_n+9), what is the value of (a_4-a_2)?ExpertLevel 44