Mathematics
Recursive rule
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.
Topic overviewटॉपिक का परिचय
Concept revisionअवधारणाओं का पुनरावर्तन
If (a_1=2) and (a_{n+1}=a_n+3), what is (a_4)?
By the recursive rule, each new term is found by adding 3 to the previous term. Thus, \(a_2=2+3=5\), \(a_3=5+3=8\), and \(a_4=8+3=11\).
If (a_1=10) and (a_{n+1}=a_n-2), what is (a_5)?
The recursive rule subtracts 2 from each preceding term: \(a_1=10\), \(a_2=8\), \(a_3=6\), \(a_4=4\), and \(a_5=2\). Therefore, the correct answer is \(2\).
If (a_1=3) and (a_{n+1}=2a_n), what is the value of (a_4)?
By the recursive rule, each new term is twice the preceding term. Thus, \(a_2=2\times3=6\), \(a_3=2\times6=12\), and \(a_4=2\times12=24\).