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=180) and (a_{n+1}=a_n-(6n+5)), what is (a_3)?HardLevel 47If (a_1=2), (a_2=4), and (a_n=4a_{n-1}-3a_{n-2}+2), what is (a_4)?HardLevel 47Which of the following recursive rules requires two initial terms to determine all the terms of a sequence?HardLevel 47If (a_1=6) and (a_{n+1}=a_n+\frac{5n}{2}), what is (a_5)?HardLevel 47If a₁ = 60 and aₙ₊₁ = aₙ − 5n/2, what is a₅?HardLevel 47If (a_1=3) and (a_{n+1}=n a_n+4), what is (a_4)?HardLevel 47Which of the following recursive rules represents an arithmetic progression (AP) with common difference \(-5\)?HardLevel 47Which recursive rule is correct for the sequence 5, 16, 49, 148, ...?HardLevel 47Which recursive rule is correct for the sequence (20, 15, 7, −8, ...)?HardLevel 47If a₁ = 7 and aₙ₊₁ = aₙ + n² + n, which term is 47?HardLevel 46If (a_1=150) and (a_{n+1}=a_n-(n^2+n)), which term is (110)?HardLevel 47If (a_1=2), (a_2=8), and (a_n=a_{n-1}+2a_{n-2}+n), what is (a_5)?HardLevel 47Which of the following recursive rules generally requires two initial terms to determine a sequence uniquely?HardLevel 47If (a_1=6) and (a_{n+1}=a_n+a_1+n^2), what is (a_4)?HardLevel 47If (a_1=6) and (a_{n+1}=a_n+a_1+n^2), what is (a_3)?HardLevel 47If (a_1=5) and (a_{n+1}=a_n+(n+1)!), what is (a_4)?HardLevel 47If (a_1=4) and (a_{n+1}=3a_n+n), what is (a_4)?ExpertLevel 44If (a_1=150) and (a_{n+1}=a_n-(n^2+2n)), what is (a_5)?ExpertLevel 44If a₁ = 2, a₂ = 5, and aₙ = 2aₙ₋₁ + 3aₙ₋₂, what is a₅?ExpertLevel 44If (a_1=1), (a_2=3), and (a_n=3a_{n-1}-a_{n-2}+n), what is (a_4)?ExpertLevel 44