Solution to MATHEMATICAL INDUCTION AND RECURRENCE 5. If P(k) = k2 (k + 2)(k – 1) is … - Sikademy
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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

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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


10. a_o represents starting value.

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Question ID: mtid-5-stid-8-sqid-3044-qpid-1743