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
Which of the following rules defines a sequence recursively?MediumLevel 44Which of the following is a recursive rule for a sequence in which each new term depends on the immediately preceding term?MediumLevel 44If (a_1=5) and (a_{n+1}=a_n+(-1)^n), what is (a_5)?MediumLevel 44If (a_1=4) and (a_{n+1}=a_n+2(-1)^n), what is (a_4)?MediumLevel 44If (a_1=4) and (a_{n+1}=a_n+2(-1)^n), what is (a_3)?MediumLevel 44If (a_1=1) and (a_{n+1}=a_n+2^n), what is (a_5)?MediumLevel 44If (a_1=100) and (a_{n+1}=a_n-2^n), what is (a_4)?MediumLevel 44If (a_1=3) and (a_{n+1}=a_n+n(n+1)), what is (a_4)?MediumLevel 44If (a_1=60) and (a_{n+1}=a_n-n(n+1)), what is (a_4)?MediumLevel 44If (a_1=2) and (a_{n+1}=a_n+2a_1), what is (a_4)?MediumLevel 44If (a_1=6) and (a_{n+1}=a_n+a_1+n), what is (a_3)?MediumLevel 44If (a_1=2), (a_2=3), and (a_n=a_{n-1}+n), what is (a_5)?MediumLevel 44If (a_1=2), (a_2=3), and (a_n=a_{n-1}+n), what is (a_4)?MediumLevel 44If (a_1=5) and (a_{n+1}=a_n+4), what is (a_7)?MediumLevel 44If a₁ = 12 and aₙ₊₁ = aₙ + 6, which term is 42?MediumLevel 44Which of the following recursive rules defines the sequence \(5,8,11,14,\ldots\)?MediumLevel 44If (a_1=3) and (a_{n+1}=2a_n+2), what is the value of (a_3-a_2)?MediumLevel 44If (a_1=2), (a_2=5), and (a_n=a_{n-1}+a_{n-2}+1), what is (a_5)?MediumLevel 44If (a_1=2), (a_2=5), and (a_n=a_{n-1}+a_{n-2}+1), what is (a_4)?MediumLevel 44If (a_1=4) and (a_{n+1}=3a_n-2), what is (a_3)?MediumLevel 44