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 of the following rules completely defines a sequence in recursive form?MediumLevel 46If a₁ = 2, a₂ = 5, and aₙ = aₙ₋₁ + 2aₙ₋₂, what is a₅?MediumLevel 46In an arithmetic sequence, the difference between every pair of consecutive terms is 3. Which recursive rule represents this sequence?MediumLevel 46If (a_1=4), (a_2=10), and (a_n=2a_{n-1}-a_{n-2}), what is (a_6)?MediumLevel 46If (a_1=6) and (a_{n+1}=a_n+n^2+2n), what is (a_4)?MediumLevel 46If (a_1=90) and (a_{n+1}=a_n-(n^2+n)), what is (a_4)?MediumLevel 46If (a_1=1) and (a_{n+1}=a_n+3^n), what is (a_4)?MediumLevel 46If (a_1=100) and (a_{n+1}=a_n-3^n), what is (a_4)?MediumLevel 46If (a_1=8) and (a_{n+1}=a_n+2(-1)^n+n), what is (a_4)?MediumLevel 46If (a_1=8) and (a_{n+1}=a_n+2(-1)^n+n), what is (a_3)?MediumLevel 46If (a_1=3) and (a_{n+1}=a_n+n(n+3)), what is (a_4)?MediumLevel 46If (a_1=3) and (a_{n+1}=a_n+n(n+3)), what is (a_3)?MediumLevel 46If (a_1=120) and (a_{n+1}=a_n-n(n+3)), what is (a_4)?MediumLevel 46If (a_1=4) and (a_{n+1}=2a_n+5), what is (a_4)?MediumLevel 46A student says that the sequence 5, 8, 11, 14, ... can be written only by an explicit formula and not by a recursive rule. Which recursive rule correctly corrects the student?MediumLevel 46If (a_1=5) and (a_{n+1}=3a_n+n+2), what is (a_2)?MediumLevel 46Which of the following recursive rules represents an arithmetic progression?MediumLevel 46If a₁ = 2 and aₙ₊₁ = aₙ + n(n + 1)/2 + 1, what is a₅?MediumLevel 46If a₁ = 2 and aₙ₊₁ = aₙ + n(n + 1)/2 + 1, what is a₄?MediumLevel 46If \(a_1=80\) and \(a_{n+1}=a_n-\frac{n(n+1)}{2}-1\), what is \(a_4\)?MediumLevel 46