Question

1·2 points Find the first six terms of the following recursively defined sequence: tk(k-1)tk-1 +2tk-2 for k 2 2 1.t1. 2. [3 points] Consider a sequence co, c, C2, . . . defined recursively ck = 3Q-1 + 1 for all k 2 1 and co 2. Use iteration to guess an explicit formula for the sequence 3. [3 points] Use mathematical induction to verify the correctness of the formula you obtained in Problem 2 4. [2 points] A certain computer algorithm executes four times as many operations when it is run with an input of size n as when it is run with an input of size n-1. Here, n > 1 is an integer. When the algorithm is run with an input of size 1, it executes 12 operations. How many operations does the algorithm execute when it is run with an input of size 5? How many operations does the algorithm execute when it is run with an input of size 10? How many operations does the algorithm execute when it is run with an input of size In

Answer 1

1. rcK ク on, t2= i + 2 (-1) Tb K-3, then. K-4, hun 3,0 +2(-リ 5-5, then 4.2) 2.0 5-6, the 6(-2) 2-C-2) 改梯