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=2) and (a_{n+1}=a_n+n^2+2n+1), what is (a_4)?MediumLevel 46If (a_1=24) and (a_{n+1}=a_n+\frac{a_n}{3}), what is (a_3)?MediumLevel 46If \(a_1=18\) and \(a_{n+1}=a_n+\frac{a_n}{3}\), what is \(a_2\)?MediumLevel 46If (a_1=1), (a_2=3), and (a_n=4a_{n-1}-3a_{n-2}), what is (a_5)?MediumLevel 46If a₁ = 1, a₂ = 3, and aₙ = 4aₙ₋₁ − 3aₙ₋₂, what is a₄?MediumLevel 46If (a_1=3) and (a_{n+1}=n a_n+2), what is (a_4)?MediumLevel 46If a₁ = 4 and aₙ₊₁ = 2aₙ + n, what is a₄?HardLevel 45If (a_1=50) and (a_{n+1}=a_n-(2n+3)), what is (a_5)?HardLevel 45Which of the following recursive rules represents an arithmetic progression with common difference 3?HardLevel 45If (a_1=2) and (a_{n+1}=a_n+n^2+2n), what is (a_5)?HardLevel 45If a₁ = 120 and aₙ₊₁ = aₙ − (n² + n), what is a₅?HardLevel 45If a₁ = 1, a₂ = 4, and aₙ = aₙ₋₁ + 2aₙ₋₂, what is a₆?HardLevel 45If a₁ = 5, a₂ = 8, and aₙ = 2aₙ₋₁ − aₙ₋₂, what is a₇?HardLevel 45If (a_1=2) and (a_{n+1}=a_n+2^n+n), what is (a_4)?HardLevel 45If a₁ = 3 and aₙ₊₁ = aₙ + 2ⁿ − n, what is a₅?HardLevel 45If a₁ = 6 and aₙ₊₁ = aₙ + (-1)ⁿ(2n), what is a₅?MediumLevel 45If (a_1=6) and (a_{n+1}=a_n+(-1)^n(2n)), what is (a_4)?HardLevel 45If (a_1=4) and (a_{n+1}=a_n+n(n+1)+2), what is (a_4)?HardLevel 45If (a_1=90) and (a_{n+1}=a_n-n(n+1)-2), what is (a_4)?HardLevel 45If (a_1=3) and (a_{n+1}=2a_n+2n+1), what is (a_4)?HardLevel 45