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
A sequence is defined by \(a_1=1\) and \(a_{n+1}=a_n+2n\). Which statement about it is correct?HardLevel 45If a₁ = 100 and aₙ₊₁ = aₙ/2 + 3n, what is a₃?HardLevel 45If \(a_1=20\) and \(a_{n+1}=\frac{a_n}{2}+3n\), what is \(a_2\)?HardLevel 45If (a_1=5) and (a_{n+1}=a_n+2a_1+n^2), what is (a_3)?HardLevel 45Suppose a sequence is defined by \(u_1=1\) and \(u_{n+1}=u_n+2n+1\). What type of sequence is it?HardLevel 45If (a_1=2), (a_2=3), and (a_n=a_{n-1}+a_{n-2}+2n), what is (a_4)?HardLevel 45Which of the following recursive rules generally requires two initial terms to determine a sequence?HardLevel 45If (a_1=4) and (a_{n+1}=a_n^2-3a_n), what is (a_3)?HardLevel 45If (a_1=3) and (a_{n+1}=a_n^2-a_n+2), what is (a_3)?HardLevel 45If (a_1=3) and (a_{n+1}=a_n^2-a_n+2), what is (a_2)?HardLevel 45If (a_1=7) and (a_{n+1}=a_n+5), what is (a_{10})?HardLevel 45Which recursive rule correctly represents a geometric sequence whose first term is 5 and in which each successive term is twice the preceding term?HardLevel 45If (a_1=6) and (a_{n+1}=2a_n+4), what is the value of (a_4-a_2)?HardLevel 45If (a_1=6) and (a_{n+1}=2a_n+4), what is the value of (a_3-a_2)?HardLevel 45If (a_1=5), (a_2=9), and (a_n=a_{n-1}+a_{n-2}+4), what is (a_5)?HardLevel 45If (a_1=5), (a_2=9), and (a_n=a_{n-1}+a_{n-2}+4), what is (a_4)?HardLevel 45For the sequence \(a_1=7\) and \(a_{n+1}=a_n+4\), which is the correct classification of the sequence?HardLevel 45Which of the following recursive rules guarantees an arithmetic progression for any initial term?HardLevel 45If a₁ = 4 and aₙ₊₁ = aₙ + 7n - 2, what is a₄?MediumLevel 45If (a_1=4) and (a_{n+1}=a_n+7n-2), what is (a_3)?HardLevel 45