DP Mathematics HL Questionbank
10.11
Description
[N/A]Directly related questions
- 18M.3dm.hl.TZ0.5a: Write down the auxiliary equation and use it to find an expression for \({f_n}\) in terms of \(n\).
- 16M.3dm.hl.TZ0.4c: Find a simplified expression for \({u_n} + {v_n}\) given that, (i) \(n\) is even. (ii) ...
- 16M.3dm.hl.TZ0.4b: Use strong induction to prove that the solution to the recurrence relation...
- 16M.3dm.hl.TZ0.4a: Solve the recurrence relation \({v_n} + 4{v_{n - 1}} + 4{v_{n - 2}} = 0\) where...
- 16N.3dm.hl.TZ0.3f: Find the smallest value of \(n\) for which \({u_n} > 100\,000\).
- 16N.3dm.hl.TZ0.3e: Find the value of \({u_{20}}\).
- 16N.3dm.hl.TZ0.3d: (i) Given that \(A = \frac{1}{{\sqrt 5 }}\left( {\frac{{1 + \sqrt 5 }}{2}} \right)\), use the...
- 16N.3dm.hl.TZ0.3c: (i) Write down the auxiliary equation for this recurrence relation. (ii) Hence find the...
- 16N.3dm.hl.TZ0.3b: Show that \({u_{n + 2}} = {u_{n + 1}} + {u_n}\).
- 16N.3dm.hl.TZ0.3a: Find the values of \({u_1},{\text{ }}{u_2},{\text{ }}{u_3}\).
- 17N.3dm.hl.TZ0.2a: Find an expression for \({u_n}\) in terms of \(n\).
- 17M.3dm.hl.TZ0.4b: Solve the recurrence relation \({u_{n + 2}} - 2{u_{n + 1}} + 5{u_n} = 0\) given that...
- 17M.3dm.hl.TZ0.4a: Verify that the recurrence relation is satisfied by \[{u_n} = A{\alpha ^n} + B{\beta...
- 15N.3dm.hl.TZ0.2c: A second recurrence relation, where \({v_1} = {u_1}\) and \({v_2} = {u_2}\), is given by...
- 15N.3dm.hl.TZ0.2b: Find an expression for \({u_n}\) in terms of \(n\).
- 15N.3dm.hl.TZ0.2a: Use the recurrence relation to find \({u_2}\).
- SPNone.3dm.hl.TZ0.5a: The sequence \(\{ {u_n}\} \) , \(n \in {\mathbb{Z}^ + }\) , satisfies the recurrence relation...
- 14M.3dm.hl.TZ0.4: (a) (i) Write down the general solution of the recurrence relation...
- 15M.3dm.hl.TZ0.3a: The sequence \(\{ {u_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 15M.3dm.hl.TZ0.3b: The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 15M.3dm.hl.TZ0.3c: The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 14N.3dm.hl.TZ0.5a: State the value of \({u_1}\).
- 14N.3dm.hl.TZ0.5d: After they have played many games, Pat comes to watch. Use your answer from part (c) to estimate...
- 14N.3dm.hl.TZ0.5b: Show that \({u_n}\) satisfies the recurrence...
- 14N.3dm.hl.TZ0.5c: Solve this recurrence relation to find the probability that Andy wins the \({n^{{\text{th}}}}\)...
Sub sections and their related questions
Recurrence relations. Initial conditions, recursive definition of a sequence.
- SPNone.3dm.hl.TZ0.5a: The sequence \(\{ {u_n}\} \) , \(n \in {\mathbb{Z}^ + }\) , satisfies the recurrence relation...
- 14M.3dm.hl.TZ0.4: (a) (i) Write down the general solution of the recurrence relation...
- 14N.3dm.hl.TZ0.5a: State the value of \({u_1}\).
- 15N.3dm.hl.TZ0.2a: Use the recurrence relation to find \({u_2}\).
- 16M.3dm.hl.TZ0.4a: Solve the recurrence relation \({v_n} + 4{v_{n - 1}} + 4{v_{n - 2}} = 0\) where...
- 16M.3dm.hl.TZ0.4b: Use strong induction to prove that the solution to the recurrence relation...
- 16M.3dm.hl.TZ0.4c: Find a simplified expression for \({u_n} + {v_n}\) given that, (i) \(n\) is even. (ii) ...
- 17N.3dm.hl.TZ0.2a: Find an expression for \({u_n}\) in terms of \(n\).
- 18M.3dm.hl.TZ0.5a: Write down the auxiliary equation and use it to find an expression for \({f_n}\) in terms of \(n\).
Solution of first- and second-degree linear homogeneous recurrence relations with constant coefficients.
- 15M.3dm.hl.TZ0.3b: The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 15M.3dm.hl.TZ0.3c: The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 15N.3dm.hl.TZ0.2c: A second recurrence relation, where \({v_1} = {u_1}\) and \({v_2} = {u_2}\), is given by...
The first-degree linear recurrence relation \({u_n} = a{u_{n - 1}} + b\) .
- 14N.3dm.hl.TZ0.5b: Show that \({u_n}\) satisfies the recurrence...
- 14N.3dm.hl.TZ0.5c: Solve this recurrence relation to find the probability that Andy wins the \({n^{{\text{th}}}}\)...
- 14N.3dm.hl.TZ0.5d: After they have played many games, Pat comes to watch. Use your answer from part (c) to estimate...
- 15M.3dm.hl.TZ0.3a: The sequence \(\{ {u_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 15M.3dm.hl.TZ0.3c: The sequence \(\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}\), satisfies the recurrence relation...
- 15N.3dm.hl.TZ0.2b: Find an expression for \({u_n}\) in terms of \(n\).
Modelling with recurrence relations.
- 14N.3dm.hl.TZ0.5a: State the value of \({u_1}\).
- 14N.3dm.hl.TZ0.5b: Show that \({u_n}\) satisfies the recurrence...
- 14N.3dm.hl.TZ0.5c: Solve this recurrence relation to find the probability that Andy wins the \({n^{{\text{th}}}}\)...
- 14N.3dm.hl.TZ0.5d: After they have played many games, Pat comes to watch. Use your answer from part (c) to estimate...
