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=3), (a_2=8), and (a_n=a_{n-1}+a_{n-2}), what is (a_4)?EasyLevel 49If \(a_1=45\) and \(a_{n+1}=\frac{a_n}{3}\), what is \(a_3\)?EasyLevel 49If (a_1=5) and (a_{n+1}=a_n+4), which term is (21)?EasyLevel 49If a₁ = 10 and aₙ₊₁ = aₙ + 5, which term is 30?EasyLevel 5Which recursive rule is correct for the sequence 12, 15, 18, 21, …?EasyLevel 49Which recursive rule is correct for the sequence (36, 31, 26, 21, ...)?EasyLevel 49What is the recursive rule for the sequence (3,15,75,375,\ldots)?EasyLevel 49Which recursive rule matches the sequence (72,24,8,\ldots)?EasyLevel 49If a₁ = 20 and aₙ₊₁ = aₙ + 1, what is a₄?EasyLevel 49If (a_1=100) and (a_{n+1}=a_n-25), what is (a_4)?EasyLevel 49If (a_1=4) and (a_{n+1}=a_n+6), what is the value of (a_5-a_2)?EasyLevel 49If (a_1=8) and (a_{n+1}=a_n+5), what is (a_2+a_4)?EasyLevel 49If (a_1=4) and (a_{n+1}=a_n^2), what is (a_2)?EasyLevel 49If (a_1=3) and (a_{n+1}=a_n^2+1), what is (a_2)?EasyLevel 49If (a_1=90) and (a_{n+1}=a_n-30), what is (a_3)?EasyLevel 49If (a_1=16) and (a_{n+1}=a_n+9), what is (a_4)?EasyLevel 49If (a_1=2) and (a_{n+1}=6a_n), what is (a_3)?EasyLevel 49Which recursive rule represents an arithmetic progression in which each successive term is 4 greater than the preceding term?EasyLevel 49If \(a_1=50\) and \(a_{n+1}=\frac{a_n}{2}+3\), what is \(a_2\)?EasyLevel 49If (a_1=1) and (a_{n+1}=a_n+5n), what is (a_4)?EasyLevel 49