MATH 2030 Quiz: MATH 2030 University of Manitoba Quiz 5

• School: University of Manitoba
• Department: Mathematics
• Course: MATH 2030
• Professor: All

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Instructor: r. craigen: time: 20 minutes no aids permitted, total marks: 20. Student number: suppose a sequence {an}n 0 satis es a cchl recurrence whose characteristic polynomial is f (x) = (x2 4)(x 3)2(x + 1)3. [3] (b) write down the general solution for this recurrence. Answer: an = 2na + ( 2)nb + (c + dn)3n + (e + f n + gn2)( 1)n: a sequence {bn}n 0 satis es the second-order cchl recurrence with characteristic polynomial. [2] (a) write down the recurrence satis ed by the sequence. Answer: g(x) = x2 3x 10, so g(x) = (x 5)(x + 2) bn = 3bn 1 + 10bn 2. [2] (b) solve this recurrence given that b0 = b2 = 7. Answer: bn = 5na + ( 2)nb so b0 = a + b = 7 and b2 = 25a + 4b = 7 so b2 4b0 = 21a = 21.