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=6) and (a_{n+1}=a_n+5n-2), what is (a_4)?MediumLevel 44If (a_1=6) and (a_{n+1}=a_n+5n-2), what is (a_3)?MediumLevel 44If (a_1=1) and (a_{n+1}=a_n+n^2+n), what is (a_4)?MediumLevel 44If (a_1=1) and (a_{n+1}=a_n+n^2+n), what is (a_3)?MediumLevel 44If (a_1=9) and (a_{n+1}=a_n+2a_n), what is (a_3)?MediumLevel 44If a₁ = 12 and aₙ₊₁ = aₙ + aₙ/2, what is a₃?MediumLevel 44If (a_1=4) and (a_{n+1}=a_n+3n), what is (a_4)?MediumLevel 45If (a_1=30) and (a_{n+1}=a_n-(2n+1)), what is (a_4)?MediumLevel 45If a₁ = 2 and aₙ₊₁ = 2aₙ + n, what is the value of a₅?MediumLevel 45If (a_1=6) and (a_{n+1}=3a_n-2), what is (a_3)?MediumLevel 45If (a_1=1) and (a_{n+1}=a_n+n^2+1), what is (a_4)?MediumLevel 45If (a_1=50) and (a_{n+1}=a_n-n^2), what is (a_5)?MediumLevel 45If (a_1=3), (a_2=5), and (a_n=a_{n-1}+2a_{n-2}), what is (a_5)?MediumLevel 45If (a_1=3), (a_2=5), and (a_n=a_{n-1}+2a_{n-2}), what is (a_4)?MediumLevel 45If (a_1=4), (a_2=9), and (a_n=2a_{n-1}-a_{n-2}), what is (a_6)?MediumLevel 45If (a_1=2) and (a_{n+1}=a_n+2^n), what is (a_5)?MediumLevel 45If (a_1=90) and (a_{n+1}=a_n-2^n), what is (a_4)?MediumLevel 45If (a_1=5) and (a_{n+1}=a_n+(-1)^{n+1}n), what is (a_5)?MediumLevel 45If (a_1=5) and (a_{n+1}=a_n+(-1)^{n+1}n), what is (a_4)?MediumLevel 45If (a_1=2) and (a_{n+1}=a_n+n(n+2)), what is (a_4)?MediumLevel 45