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 = 150 and aₙ₊₁ = aₙ - (5n + 4), what is a₄?MediumLevel 45If (a_1=150) and (a_{n+1}=a_n-(5n+4)), what is (a_3)?HardLevel 45If (a_1=1), (a_2=2), and (a_n=3a_{n-1}-2a_{n-2}+1), what is (a_4)?HardLevel 45Which of the following recursive rules, with \(a_1=5\), defines an arithmetic progression with common difference 3?HardLevel 45If (a_1=5) and (a_{n+1}=a_n+\frac{3n}{2}), what is (a_5)?HardLevel 45If (a_1=40) and (a_{n+1}=a_n-\frac{3n}{2}), what is (a_5)?HardLevel 45If (a_1=2) and (a_{n+1}=n a_n+3), what is (a_4)?HardLevel 45Let \(r\) be a constant and \(a_1\ne 0\). Which of the following recursive rules necessarily makes the sequence a geometric progression?HardLevel 45Which recursive rule is correct for the sequence (3,8,18,38,\ldots)?HardLevel 45Which recursive rule is correct for the sequence (10,17,31,59,\ldots)?HardLevel 45If a₁ = 5 and aₙ₊₁ = aₙ + n², which term is 35?MediumLevel 45If (a_1=100) and (a_{n+1}=a_n-n^2), which term is (70)?HardLevel 45If (a_1=2), (a_2=7), and (a_n=a_{n-1}+a_{n-2}+n), what is (a_5)?HardLevel 45If (a_1=2), (a_2=7), and (a_n=a_{n-1}+a_{n-2}+n), what is (a_4)?HardLevel 45If (a_1=9) and (a_{n+1}=a_n+a_1+n^2), what is (a_3)?HardLevel 45If (a_1=9) and (a_{n+1}=a_n+a_1+n^2), what is (a_2)?HardLevel 45If (a_1=6) and (a_{n+1}=2a_n+n), what is (a_4)?HardLevel 46If a₁ = 80 and aₙ₊₁ = aₙ − (3n + 2), what is a₅?HardLevel 46If (a_1=1) and (a_{n+1}=a_n+n^2+3n), what is (a_5)?HardLevel 46Which recursive rule necessarily generates an arithmetic progression if the initial term \(a_1\) is any real number?HardLevel 46