Answer to Question #187961 in Discrete Mathematics for Maricel

Question

 MATHEMATICAL INDUCTION AND RECURRENCE 

5. If P(k) = k2 (k + 2)(k – 1) is true, then what is P (k + 1)? (2 pts)

A. (k + 1)2 (k + 2)(k)

B. (k + 1)2 (k + 2)(k)

C. (k + 1)(k + 3)(k)

D. (k + 1)2 (k + 3)(k)

6. Using the principle of mathematical induction, 2n-1 is divisible by which of

the following? (2 pts)

A. 1

B. 0

C. 4

D. ½ 

7. A relation represents an equation where the next term is dependent on the

previous term is called

A. Binomial relation

B. Recurrence relation

C. Regression relation

D. None of these

8. Calculate the value of a2 for the recurrence relation an=17an-1+30n, where

a0=3. (2 pts)

A. 2346

B. 1296

C. 1437

D. 5484

9. The recurrence relation for Fibonacci sequence is

A. Fn = Fn + 1

+ Fn - 2

B. Fn = Fn - 1

+ Fn - 2

C. Fn = Fn - 1

- Fn - 2

D. None of these

10. In recurrence relation, a0 represents

A. Current value

B. Starting value

C. The value of next term in the sequence

D. None of these 

Answer 1

5. $P(k)=k^2(k+2)(k-1)$

    then, $P(k+1)=(k+1)^2(k+3)k$

     

option (D) is correct.

6. $2n-1$ is a odd number which is divisible by 1.

so option (A) is correct 

7.(B) Recurrence Relation

8. $a_n=17a_{n-1}+30n$

   

 at $n=1, a_1=17a_o=17(3)=51$

 at $n=2, a_2=17a_1+30=17(51)+60=867+60=927$

9.(B)$F_n=F_{n-1}+F_{n-2}$

10. $a_o$ represents starting value.