MAD 2104 Midterm: MAD 2104 FIU ds Test 2a aspr 00
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Suppose matrices a, b, and c are as given below. Then (b) give a recursive definition of the sequence {an}, where n = 1,2,3, if an = 2n + 1. quantification used in the induction step. ] Induction step: ( n)(n + an+1 = an + 2) or ( n +)(an+1 = an + 2). [be very careful of the (c) give a recursive definition of the set s of positive integers that are multiples of 3. Induction step: ( x)( x s x+3 s ) ( x)( y)( (x s y s ) x+y s ) Basis step: 3 s or alternatively: (10 pts. ) Let {an} be defined by the formula n = 1,2,3, Define the sequence {bn} recursively by b1 = 7 and bn+1 = bn + 5 for n = 1,2,3, an = bn for n = 1,2,3, Basis step: evidently, a1 = 5(1) + 2 = 7 = b1.
