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
Which recursive rule is correct for the sequence (4,13,40,121,\ldots)?HardLevel 46Which recursive rule is correct for the sequence (9,7,10,6,\ldots)?HardLevel 46If a₁ = 8 and aₙ₊₁ = aₙ/2 + a₁, what is a₄?HardLevel 46If (a_1=7) and (a_{n+1}=a_n+na_1), what is (a_4)?HardLevel 46If a₁ = 2, a₂ = 5, and aₙ = 2aₙ₋₁ + aₙ₋₂ + n, what is a₄?HardLevel 46If (a_1=100) and (a_{n+1}=a_n-(2^n+n^2+n)), what is (a_4)?HardLevel 46If (a_1=5) and (a_{n+1}=2a_n+n^2), what is (a_4)?HardLevel 47If (a_1=100) and (a_{n+1}=a_n-(2n^2+n)), what is (a_4)?HardLevel 47If (a_1=100) and (a_{n+1}=a_n-(2n^2+n)), what is (a_3)?HardLevel 47If (a_1=2), (a_2=7), and (a_n=2a_{n-1}+a_{n-2}), what is (a_5)?HardLevel 47If a₁ = 2, a₂ = 7, and aₙ = 2aₙ₋₁ + aₙ₋₂, what is a₄?HardLevel 47If a₁ = 4, a₂ = 10, and aₙ = 3aₙ₋₁ − 2aₙ₋₂, what is a₅?HardLevel 47If (a_1=3) and (a_{n+1}=a_n+3^n+n^2), what is (a_4)?HardLevel 47If (a_1=3) and (a_{n+1}=a_n+3^n+n^2), what is (a_3)?HardLevel 47If (a_1=150) and (a_{n+1}=a_n-(2^n+n^2)), what is (a_5)?HardLevel 47If a₁ = 150 and aₙ₊₁ = aₙ − (2ⁿ + n²), what is a₄?HardLevel 47If (a_1=12) and (a_{n+1}=a_n+(-1)^n(3n+1)), what is (a_5)?HardLevel 47If (a_1=12) and (a_{n+1}=a_n+(-1)^n(3n+1)), what is (a_4)?HardLevel 47If (a_1=6) and (a_{n+1}=a_n+n(n+4)+2), what is (a_4)?HardLevel 47If (a_1=6) and (a_{n+1}=a_n+n(n+4)+2), what is (a_3)?HardLevel 47