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 = 8, a₂ = 13, and each next term is the sum of the previous two terms, what is a₆?MediumLevel 42In the sequence \((2,3,5,8,13,\ldots)\), each term is the sum of the previous two terms. What is the eighth term?MediumLevel 44In the sequence \((1,2,4,7,11,\ldots)\), the added numbers are \((1,2,3,4,\ldots)\). What is the eighth term?MediumLevel 44In the sequence (15, 12, 7, 0, -9, ...), the differences are (-3, -5, -7, -9, ...). What will be the next term?MediumLevel 44In the sequence (7, 15, 31, 63, 127, ...), each next term is obtained by doubling the previous term and adding 1. What will be the next term?MediumLevel 42In the sequence (2, 3, 5, 9, 17, 33, ...), each next term is obtained by doubling the previous term and subtracting 1. What will be the next term?MediumLevel 43If (a_1=2) and (a_{n+1}=a_n+3), what is (a_4)?EasyLevel 47If (a_1=10) and (a_{n+1}=a_n-2), what is (a_5)?EasyLevel 47If (a_1=3) and (a_{n+1}=2a_n), what is the value of (a_4)?EasyLevel 47If \(a_1=64\) and \(a_{n+1}=\frac{a_n}{2}\), what is \(a_4\)?EasyLevel 47If (a_1=1) and (a_{n+1}=a_n+n), what is (a_5)?EasyLevel 47If (a_1=20) and (a_{n+1}=a_n-n), what is the value of (a_4)?EasyLevel 47If (a_1=4) and (a_{n+1}=a_n+2n), what is (a_4)?EasyLevel 47If (a_1=5) and (a_{n+1}=a_n+(2n-1)), what is (a_4)?EasyLevel 47If (a_1=2) and (a_{n+1}=3a_n), what is (a_3)?EasyLevel 47If (a_1=1) and (a_{n+1}=2a_n+1), what is (a_4)?EasyLevel 47If (a_1=5) and (a_{n+1}=2a_n-1), what is the value of (a_3)?EasyLevel 47If (a_1=2) and (a_{n+1}=a_n+5), what is (a_6)?EasyLevel 47If (a_1=30) and (a_{n+1}=a_n-4), what is (a_5)?EasyLevel 47If (a_1=2), (a_2=3), and (a_n=a_{n-1}+a_{n-2}), what is (a_5)?EasyLevel 47