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=3) and (a_{n+1}=a_n+n^3), what is (a_5)?ExpertLevel 44If (a_1=150) and (a_{n+1}=a_n-n^3), what is (a_5)?ExpertLevel 44Which recursive rule is correct for the sequence 3, 8, 19, 46, …?HardLevel 44If (a_1=4), (a_2=6), and (a_n=a_{n-1}+3a_{n-2}+n), what is (a_4)?ExpertLevel 44If (a_1=2) and (a_{n+1}=(n+1)a_n+n), what is (a_4)?ExpertLevel 41In a sequence, (a_1=3) and (a_n=2a_{n-1}+1). What will be the value of (a_4)?ExpertLevel 44In a sequence, (t_1=2), (t_2=5), and (t_n=t_{n-1}+2t_{n-2}). What will be the value of (t_5)?ExpertLevel 44In a sequence, (a_1=3) and (a_n=2a_{n-1}+n+1). What is the value of (a_4)?ExpertLevel 45In a sequence, b₁ = 6 and bₙ = 3bₙ₋₁ − n. What is the value of b₄?MediumLevel 45In a sequence, (c_1=1), (c_2=3), and (c_n=2c_{n-1}+c_{n-2}). What is the value of (c_5)?ExpertLevel 45If (d_n=d_{n-1}+2n) and (d_4=25), what is the value of (d_1)?ExpertLevel 45Which recursive rule is correct for the sequence (4), (9), (19), (39)?ExpertLevel 45If (f_1=10) and (f_n=f_{n-1}-n), which will be the first negative term?ExpertLevel 45In a sequence, (g_1=2) and (g_n=g_{n-1}+2n-1). What is the value of (g_5)?ExpertLevel 45If (h_1=3) and (h_n=n h_{n-1}), what is the value of (h_4)?ExpertLevel 45In a sequence, (j_1=1) and (j_n=j_{n-1}+n^2). What is the value of (j_4)?ExpertLevel 45If \(k_1=64\) and \(k_n=\frac{k_{n-1}}{2}+n\), what is the value of \(k_4\)?ExpertLevel 45In a sequence, (m_1=2) and (m_n=m_{n-1}+3n). What is the value of (m_4)?ExpertLevel 45If (n_1=5) and (n_n=2n_{n-1}-n^2), what is the value of (n_4)?ExpertLevel 45If (r_1=1), (r_2=2), and (r_n=r_{n-1}+3r_{n-2}), what is the value of (r_5)?ExpertLevel 45