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
In a sequence, (R_1=2) and (R_n=nR_{n-1}+n). What is the value of (R_4)?ExpertLevel 45If (O_1=4) and (O_n=O_{n-1}+2^n+n), what is the value of (O_4)?ExpertLevel 45In a sequence, (P_1=3) and (P_n=P_{n-1}+4n-3). What is the value of (P_5)?ExpertLevel 45If (Q_1=2), (Q_2=5), and (Q_n=Q_{n-1}+2Q_{n-2}+n), what is the value of (Q_5)?ExpertLevel 45If (R_1=1) and (R_n=R_{n-1}^2+n), what is the value of (R_3)?ExpertLevel 45In a sequence, (S_1=100) and (S_n=S_{n-1}-n^2). What is the value of (S_4)?ExpertLevel 45If (T_1=2) and (T_n=(n+1)T_{n-1}-n), what is the value of (T_4)?ExpertLevel 45Which option gives a complete recursive definition of a sequence?ExpertLevel 45If (a_n=a_{n-1}+3n) and (a_4=31), what is the value of (a_2)?ExpertLevel 45If (b_n=2b_{n-1}+n) and (b_3=19), what is the value of (b_1)?ExpertLevel 45If (c_1=2) and (c_n=c_{n-1}+n^2), which statement is correct?ExpertLevel 45If (d_1=1) and (d_n=d_{n-1}+3n), for which (n) will (d_n>40) first occur?ExpertLevel 45If (e_1=3) and (e_n=2e_{n-1}+n), what is the value of (e_5-e_4)?ExpertLevel 45If (f_1=2) and (f_n=f_{n-1}+2n), what is the sum of the first four terms?ExpertLevel 45If (g_1=1) and (g_n=3g_{n-1}-1), what is (g_4:g_3)?ExpertLevel 45If (h_1=2), (h_2=7), and (h_n=2h_{n-1}-h_{n-2}+3), what is the value of (h_5)?ExpertLevel 45If (p_1=1) and (p_n=p_{n-1}+n^2-n), what is the value of (p_5)?ExpertLevel 45In a sequence, (a_1=4) and (a_n=2a_{n-1}+n+2). What is the value of (a_5)?ExpertLevel 46In a sequence, b₁ = 7 and bₙ = 3bₙ₋₁ − 2n + 1. What is the value of b₄?ExpertLevel 46If (c_1=2), (c_2=5), and (c_n=c_{n-1}+2c_{n-2}+n), what is the value of (c_5)?ExpertLevel 46