I\'m aware of chegg\'s policy but please, these are simple MCQ\'s. Answer can be

Question

I'm aware of chegg's policy but please, these are simple MCQ's.

Answer can be NONE as well

1: A graph is encoded as a string by listing the number of vertices, followed by a semi-colon, followed by a list of the edges in the graph. The graph encoding is used to define a language L: A string is in the language if and only if the string is a valid encoding of a graph and the graph contains a path in which every vertex appears exactly once. Select the string that is in the language. fa that s in the lantains a pa ?. 413, 4). (4, 2), (2, 1), (1,3), (2, 2). (3, 1) 5,16. 4-4 2 212 2: Select the problem that is a decision problem. a. Given a graph, determine the length of the longest cycle in the graph. b. Given a graph and a positive integer x, determine whether the graph has a cycle of length x. c. Given a graph, find the longest cycle in the graph. d. Given a graph, determine the number of distinct cycles of length 3 that the graph contains. Chapter 8 Induction and Recursion 8.1 Sequences 3: Select the description that fits the sequence below: 8, 5, 2,2, 1,-1 a. Non-decreasing but not increasing C. Non-increasing but not decreasing 4: What is the common ratio of the following geometric sequence? 27, 9, 3, 1, a. 27 b. 9 d. 1/3 5: The sequence ff) starts with an index of 1 and is defined so that fn is the largest integer k such that k sn. Which sequence fits the definition of (th)? a. 1.4, 9, 16, 25,.. c. 2, 4, 8, 16, 32,. d. 1. 2, 3, 4, 5, Page 1 of 9 HW-6 8.2 Recurrence relations 6: A sequence {a) is defined as follows: ao#2, ?,-1, and for n22. a.-3 a-'-n an2 + 1 . What is b.-1 C. d. 2 7: A sequence is defined by the recurrence relation fr n fn-1-foa. How many initial values are required so that the sequence is well defined for all n20? b. 1 c. 2 8: A population of mica increases by 10% every year. Define gn to bo the number of mice after n years. Select the recurenoe relation that describes the sequence (g) C. g.-(0.01) gmt gh2

Explanation / Answer

4. The common ratio is 3

Divide a term with its preceding term to get the common ratio.

So, 27/9 = 3.

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6. a3 = -2

a2 = 3.a1 - 2.a0 + 1

a2 = 3.1 - 2.2 + 1 = 0.

S0, a0 = 2; a1 = 1; a2 = 0;

And

a3 = 3 . a2 - 3 . a1 +1

a3 = 3 . 0 - 3 . 1 +1

a3 = -2;

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