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=25) and (a_{n+1}=a_n-(2n+1)), what is (a_3)?EasyLevel 47If (a_1=2), (a_2=5), and (a_n=a_{n-1}+2), what is (a_4)?EasyLevel 47If (a_1=1), (a_2=2), and (a_n=2a_{n-1}), what is (a_5)?EasyLevel 47If (a_1=3), (a_2=5), and (a_n=a_{n-1}+a_{n-2}), what is (a_6)?EasyLevel 47According to the recursive rule in the sequence (4, 7, 10, 13, ...), what is the next term?EasyLevel 47According to the recursive rule in the sequence (32, 16, 8, 4, ...), what is the next term?EasyLevel 47For the sequence (6,12,18,24,\ldots), (a_1=6). What is added in the recursive rule?EasyLevel 47For the sequence (18,15,12,9,\ldots), what is subtracted in the recursive rule?EasyLevel 47In the sequence (3,9,27,81,\ldots), what is the multiplier in the recursive rule?EasyLevel 47If (a_1=11) and (a_{n+1}=a_n+7), what is (a_3)?EasyLevel 47If (a_1=5) and (a_{n+1}=a_n+9), what is the value of (a_4)?EasyLevel 47If (a_1=90) and (a_{n+1}=\frac{a_n}{3}), what is (a_4)?EasyLevel 47If a₁ = 90 and aₙ₊₁ = aₙ ÷ 3, what is a₃?EasyLevel 47If (a_1=2) and (a_{n+1}=a_n+n+1), what is (a_4)?EasyLevel 47If (a_1=3) and (a_{n+1}=a_n+2n+2), what is (a_3)?EasyLevel 47If a₁ = 4, a₂ = 6, and aₙ = aₙ₋₁ + aₙ₋₂, what is a₅?EasyLevel 47If (a_1=4) and (a_{n+1}=a_n+2), what is (a_5)?EasyLevel 48If (a_1=18) and (a_{n+1}=a_n-3), what is (a_4)?EasyLevel 48If (a_1=5) and (a_{n+1}=2a_n), what is the value of (a_3)?EasyLevel 48If \(a_1=48\) and \(a_{n+1}=\frac{a_n}{2}\), what is \(a_5\)?EasyLevel 48