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=40) and (a_{n+1}=a_n-(n+3)), what is (a_3)?EasyLevel 49If (a_1=6), (a_2=10), and (a_n=a_{n-1}+4), what is (a_5)?EasyLevel 49If a₁ = 1, a₂ = 4, and aₙ = 2aₙ₋₁, what is a₅?EasyLevel 49If (a_1=2), (a_2=9), and (a_n=a_{n-1}+a_{n-2}), what is (a_6)?EasyLevel 49If (a_1=2), (a_2=9), and (a_n=a_{n-1}+a_{n-2}), what is (a_5)?EasyLevel 49According to the recursive rule in the sequence (11, 16, 21, 26, ...), what is the next term?EasyLevel 49According to the recursive rule in the sequence (80,40,20,10,\ldots), what will be the next term?EasyLevel 49For the sequence (9,18,27,36,\ldots), (a_1=9). What is added in the recursive rule?EasyLevel 49For the sequence (55,44,33,22,\ldots), what is subtracted in the recursive rule?EasyLevel 49In the sequence (4,24,144,864,\ldots), what is the multiplier in the recursive rule?EasyLevel 49If (a_1=18) and (a_{n+1}=a_n+8), what is (a_3)?EasyLevel 49If (a_1=7) and (a_{n+1}=a_n+12), what is the value of (a_4)?EasyLevel 49If \(a_1=128\) and \(a_{n+1}=\frac{a_n}{4}\), what is \(a_3\)?EasyLevel 49If a_1 = 2, a_2 = 6, and a_n = a_{n-1} + a_{n-2}, what is a_6?EasyLevel 49If (a_1=10) and (a_{n+1}=a_n+n+2), what is (a_4)?EasyLevel 49If (a_1=10) and (a_{n+1}=a_n+n+2), what is (a_3)?EasyLevel 49If (a_1=3) and (a_{n+1}=a_n+2n+1), what is (a_5)?MediumLevel 44If (a_1=40) and (a_{n+1}=a_n-3n), what is (a_4)?MediumLevel 44If a₁ = 2 and aₙ₊₁ = 2aₙ + n, what is the value of a₄?MediumLevel 44If (a_1=5) and (a_{n+1}=2a_n-2n), what is (a_4)?MediumLevel 44