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) and (a_{n+1}=n a_n+2n), what is (a_4)?HardLevel 46If (a_1=2) and (a_{n+1}=(n+1)a_n-1), what is (a_4)?HardLevel 46If a₁ = 200 and aₙ₊₁ = aₙ − (2ⁿ + n²), what is a₄?HardLevel 46If (a_1=1) and (a_{n+1}=a_n+3^n+n), what is (a_4)?HardLevel 46If (a_1=2), (a_2=3), and (a_n=2a_{n-1}+3a_{n-2}), what is (a_4)?HardLevel 46If (a_1=1), (a_2=5), and (a_n=2a_{n-1}-a_{n-2}+2), what is (a_5)?HardLevel 46If \(a_1=4\) and \(a_{n+1}=a_n+\frac{n(n+3)}{2}\), what is \(a_5\)?HardLevel 46If \(a_1=90\) and \(a_{n+1}=a_n-\frac{n(n+3)}{2}\), what is \(a_4\)?HardLevel 46If \(a_1=6\) and \(a_{n+1}=a_n+\frac{a_n}{2}+n\), what is \(a_3\)?HardLevel 46If (a_1=4) and (a_{n+1}=a_n+\frac{a_n}{4}+n), what is (a_3)?HardLevel 46If (a_1=2) and (a_{n+1}=a_n^2+n), what is (a_3)?HardLevel 46If (a_1=3) and (a_{n+1}=a_n^2-n), what is (a_3)?HardLevel 46Which of the following recursive rules generates a sequence in which each subsequent term depends on both the immediately preceding term and the term number?HardLevel 46If (a_1=3), (a_2=4), and (a_n=3a_{n-1}-a_{n-2}+n), what is (a_4)?HardLevel 46If (a_1=5) and (a_{n+1}=2a_n+(-1)^n), what is (a_4)?HardLevel 46If (a_1=30) and (a_{n+1}=a_n-(-1)^n(2n+1)), what is (a_4)?HardLevel 46If (a_1=3) and (a_{n+1}=a_n+n!), what is (a_5)?HardLevel 46If (a_1=100) and (a_{n+1}=a_n-n!), what is (a_5)?HardLevel 46If (a_1=1) and (a_{n+1}=2a_n+n^2), what is (a_4)?HardLevel 46A sequence is defined by the recursive rule \(a_{n+1}=a_n+2n\), where \(n\geq 1\). Which statement about this sequence must be true?HardLevel 46