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 dₙ = dₙ₋₁ + 5n − 1 and d₅ = 79, what is the value of d₁?ExpertLevel 46Which recursive rule is correct for the sequence (6), (14), (30), (62)?ExpertLevel 46If (f_1=4) and (f_n=2f_{n-1}+3), for which (n) will (f_n>150) first occur?ExpertLevel 46In a sequence, g₁ = 10 and gₙ = gₙ₋₁ + (−1)ⁿn². What is the value of g₅?ExpertLevel 46If (h_1=2) and (h_n=(n-1)h_{n-1}+3), what is the value of (h_4)?ExpertLevel 46Which information is required to determine a first-order recursive sequence uniquely?ExpertLevel 46If \(k_1=80\) and \(k_n=\frac{k_{n-1}}{2}+n\), what is the value of \(k_5\)?ExpertLevel 46In a sequence, (m_1=2) and (m_n=3m_{n-1}+n-2). What is the value of (m_4)?ExpertLevel 46If (N_1=8) and (N_n=2N_{n-1}-n(n-1)), what is the value of (N_4)?ExpertLevel 46If (r_1=4), (r_2=6), and (r_n=2r_{n-1}-r_{n-2}+n), what is the value of (r_5)?ExpertLevel 46In a sequence, s₁ = 5 and sₙ = sₙ₋₁ + (−1)ⁿ⁺¹(2n − 1). What is the value of s₅?ExpertLevel 46If (t_1=x), (t_n=2t_{n-1}+3), and (t_4=61), what is the value of (x)?ExpertLevel 46Which recursive rule is correct for the sequence (7), (17), (37), (77)?ExpertLevel 46If (v_1=3) and (v_n=v_{n-1}+n^3), what is the value of (v_4)?ExpertLevel 46In a sequence, (w_1=1) and (w_n=w_{n-1}+3^{n-1}+1). What is the value of (w_4)?ExpertLevel 46If (x_1=4) and (x_n=2x_{n-1}+n^2-n), what is the value of (x_4)?ExpertLevel 46In a sequence, (y_1=2) and (y_n=y_{n-1}+(2n-1)^2). What is the value of (y_4)?ExpertLevel 46If (z_1=1), (z_2=3), and (z_n=z_{n-1}z_{n-2}+n), what is the value of (z_5)?ExpertLevel 46In a sequence, (A_1=2) and (A_n=(n+1)A_{n-1}+2). What is the value of (A_3)?ExpertLevel 46If (B_1=11) and (B_n=B_{n-1}+2^n-n), what is the value of (B_4)?ExpertLevel 46