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=9), and (a_n=a_{n-1}+a_{n-2}+7), what is (a_5)?ExpertLevel 44If (a_1=2) and (a_{n+1}=7a_n-4), what is (a_3)?ExpertLevel 44If (a_1=6) and (a_{n+1}=a_n+9n-4), what is (a_4)?ExpertLevel 44If (a_1=210) and (a_{n+1}=a_n-(7n+6)), what is (a_4)?ExpertLevel 44If (a_1=2), (a_2=3), and (a_n=5a_{n-1}-4a_{n-2}+3), what is (a_4)?ExpertLevel 44If (a_1=7) and (a_{n+1}=a_n+\frac{7n}{2}), what is (a_5)?ExpertLevel 44If a₁ = 80 and aₙ₊₁ = aₙ − 7n/2, what is a₅?HardLevel 44If (a_1=4) and (a_{n+1}=n a_n+5), what is (a_4)?ExpertLevel 44If (a_1=5) and (a_{n+1}=(n+2)a_n-1), what is (a_4)?ExpertLevel 44Which recursive rule is correct for the sequence (4,14,44,134,\ldots)?ExpertLevel 44Which recursive rule is correct for the sequence 6, 11, 19, 30, …?MediumLevel 44If a₁ = 5 and aₙ₊₁ = aₙ + n², which term is 60?HardLevel 44If (a_1=5) and (a_{n+1}=a_n+n!+2^n), what is (a_5)?ExpertLevel 44If a₁ = 120 and aₙ₊₁ = aₙ − (n! + 2ⁿ), what is a₅?ExpertLevel 44If (a_1=4) and (a_{n+1}=2a_n+(-1)^n(2n+1)), what is (a_4)?ExpertLevel 44If (a_1=50) and (a_{n+1}=a_n-(-1)^n(n^2+1)), what is (a_4)?ExpertLevel 44If (a_1=2), (a_2=5), and (a_n=2a_{n-1}+a_{n-2}+2n), what is (a_5)?ExpertLevel 44If (a_1=6) and (a_{n+1}=a_n+a_1+n(n+1)), what is (a_4)?ExpertLevel 44If (a_1=3) and (a_{n+1}=a_n+(2n+1)^2), what is (a_4)?ExpertLevel 44If (a_1=180) and (a_{n+1}=a_n-(2n+1)^2), what is (a_4)?ExpertLevel 44