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, (C_1=4) and (C_n=C_{n-1}+n(n+2)). What is the value of (C_4)?ExpertLevel 46If (D_1=5) and (D_n=3D_{n-1}-(n+1)), what is the value of (D_4)?ExpertLevel 46If (E_1=2), (E_2=4), and (E_n=E_{n-1}+E_{n-2}+n), what is the value of (E_5)?ExpertLevel 46In a sequence, (F_1=90) and (F_n=F_{n-1}-n(n+1)). What is the value of (F_4)?ExpertLevel 46If (G_1=1) and (G_n=2G_{n-1}+2n+1), what is the value of (G_4)?ExpertLevel 46Which of the following is a second-order recursive rule that requires two initial terms to determine a sequence uniquely?ExpertLevel 46If (J_1=40) and (J_n=J_{n-1}-4(n-1)+1), what is the value of (J_5)?ExpertLevel 46If (K_1=2), (K_2=5), and (K_n=3K_{n-1}-K_{n-2}), what is the value of (K_5)?ExpertLevel 46In a sequence, (L_1=4) and (L_n=L_{n-1}+5n-4). What is the value of (L_5)?ExpertLevel 46If (M_1=2) and (M_n=4M_{n-1}-n), what is the value of (M_3)?ExpertLevel 46In a sequence, (R_1=1) and (R_n=(n+2)R_{n-1}-1). What is the value of (R_4)?ExpertLevel 46If (O_1=5) and (O_n=O_{n-1}+2^n+2n), what is the value of (O_4)?ExpertLevel 46In a sequence, (P_1=0) and (P_n=P_{n-1}+3n^2-1). What is the value of (P_4)?ExpertLevel 46If (Q_1=1), (Q_2=2), and (Q_n=Q_{n-1}+Q_{n-2}+n^2), what is the value of (Q_5)?ExpertLevel 46If (U_1=3) and (U_n=U_{n-1}^2-n), what is the value of (U_3)?ExpertLevel 46In a sequence, (S_1=75) and (S_n=S_{n-1}-2^n). What is the value of (S_4)?ExpertLevel 46If (T_1=2) and (T_n=(n+2)T_{n-1}+n), what is the value of (T_3)?ExpertLevel 46In a sequence, each new term is obtained by adding a fixed number to the immediately preceding term. What type of sequence is it?ExpertLevel 46If aₙ = aₙ₋₁ + 4n − 2 and a₅ = 70, what is the value of a₂?ExpertLevel 46If (b_n=3b_{n-1}+2) and (b_3=44), what is the value of (b_1)?ExpertLevel 46