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, s₁ = 3 and sₙ = sₙ₋₁ + (−1)ⁿn. What is the value of s₅?MediumLevel 45If (t_1=x), (t_n=t_{n-1}+n), and (t_5=24), what is the value of (x)?ExpertLevel 45Which recursive rule is correct for the sequence (2), (6), (18), (54)?ExpertLevel 45If (v_1=4) and (v_n=2v_{n-1}-1), what is the value of (v_5)?ExpertLevel 45In a sequence, (w_1=0) and (w_n=w_{n-1}+2^{n-1}). What is the value of (w_5)?ExpertLevel 45If (x_1=1) and (x_n=2x_{n-1}+n^2), what is the value of (x_3)?ExpertLevel 45In a sequence, (y_1=7) and (y_n=y_{n-1}+(n-1)^2). What is the value of (y_5)?ExpertLevel 45If (z_1=2), (z_2=3), and (z_n=z_{n-1}z_{n-2}+1), what is the value of (z_5)?ExpertLevel 45In a sequence, (A_1=1) and (A_n=nA_{n-1}+1). What is the value of (A_4)?ExpertLevel 45If (B_1=9) and (B_n=B_{n-1}+2^n), what is the value of (B_4)?ExpertLevel 45In a sequence, (C_1=5) and (C_n=C_{n-1}+n(n-1)). What is the value of (C_4)?ExpertLevel 45If (D_1=2) and (D_n=2D_{n-1}+n-1), what is the value of (D_4)?ExpertLevel 45If (E_1=1), (E_2=4), and (E_n=E_{n-1}+E_{n-2}+2), what is the value of (E_5)?ExpertLevel 45In a sequence, F₁ = 20 and Fₙ = Fₙ₋₁ − 2n + 1. What is the value of F₅?MediumLevel 45If (G_1=3) and (G_n=n+2G_{n-1}), what is the value of (G_4)?ExpertLevel 45In a sequence, (H_1=2) and (H_n=H_{n-1}+n(n+1)). What is the value of (H_4)?ExpertLevel 45If (J_1=50) and (J_n=J_{n-1}-3(n-1)), what is the value of (J_5)?ExpertLevel 45If (K_1=1), (K_2=1), and (K_n=2K_{n-1}+K_{n-2}), what is the value of (K_5)?ExpertLevel 45In a sequence, (L_1=6) and (L_n=L_{n-1}+2n+1). What is the value of (L_5)?ExpertLevel 45If (M_1=1) and (M_n=3M_{n-1}+n), what is the value of (M_3)?ExpertLevel 45