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 = 200 and aₙ₊₁ = aₙ − n(n + 4) − 2, what is a₄?HardLevel 47If (a_1=4) and (a_{n+1}=2a_n+4n-1), what is (a_4)?HardLevel 47Which of the following rules completely defines a sequence recursively?HardLevel 47If \(a_1=96\) and \(a_{n+1}=\frac{a_n}{2}+n^2+n\), what is \(a_3\)?HardLevel 47If \(a_1=24\) and \(a_{n+1}=\frac{a_n}{3}+n^2\), what is \(a_3\)?HardLevel 47If (a_1=10) and (a_{n+1}=a_n+2a_1+n^2), what is (a_3)?HardLevel 47If (a_1=2), (a_2=6), and (a_n=a_{n-1}+a_{n-2}+3n), what is (a_5)?HardLevel 47If (a_1=2), (a_2=6), and (a_n=a_{n-1}+a_{n-2}+3n), what is (a_4)?HardLevel 47If (a_1=3) and (a_{n+1}=a_n^2-2a_n+3), what is (a_3)?HardLevel 47If (a_1=4) and (a_{n+1}=a_n^2-a_n+1), what is (a_2)?HardLevel 47If (a_1=11) and (a_{n+1}=a_n+7), which term is (74)?HardLevel 47If (a_1=9) and (a_{n+1}=a_n+8), what is (a_{12})?HardLevel 47If (a_1=4) and (a_{n+1}=2a_n+7), what is the value of (a_4-a_2)?HardLevel 47If (a_1=4) and (a_{n+1}=2a_n+7), what is the value of (a_3-a_2)?HardLevel 47If (a_1=4), (a_2=8), and (a_n=a_{n-1}+a_{n-2}+6), what is (a_5)?HardLevel 47If (a_1=4), (a_2=8), and (a_n=a_{n-1}+a_{n-2}+6), what is (a_4)?HardLevel 47Which of the following recursive rules will generate an arithmetic progression with common difference \(4\), for any initial term \(a_1\)?HardLevel 47If (a_1=5) and (a_{n+1}=a_n+8n-3), what is (a_4)?HardLevel 47If (a_1=5) and (a_{n+1}=a_n+8n-3), what is (a_3)?HardLevel 47If a₁ = 180 and aₙ₊₁ = aₙ − (6n + 5), what is a₄?HardLevel 47