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# hw8sol - SolutiontoHomework8 Problem1 a b c d e...

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Solution to Homework 8 Problem 1. a) a 0 =-­૒1, a 1 =2, a 2 =-­૒4, a 3 =8, a 4 =-­૒16, a 5 =32 b) a 0 =2, a 1 =-­૒1, a 2 =-­૒3, a 3 =-­૒2, a 4 =1, a 5 =3 c) a 0 =1, a 1 =3, a 2 =27, a 3 =2187, a 4 =3 15 , a 5 =3 31 d) a 0 =-­૒1, a 1 =0, a 2 =1, a 3 =3, a 4 =13, a 5 =74 e) a 0 =1, a 1 =1, a 2 =2, a 3 =2, a 4 =1, a 5 =1 Problem 2. a) 0=a n =-­૒3a n-­૒1 +4a n-­૒2 =0+0=0=a n b) 1=a n =-­૒3a n-­૒1 +4a n-­૒2 =-­૒3*1+4*1=1=a n c) (-­૒4) n =a n =-­૒3*(-­૒4) n-­૒1 +4*(-­૒4) n-­૒2 =(-­૒4) n-­૒2 (-­૒4*(-­૒3)+4)=(-­૒4) n-­૒2 *(-­૒4) 2 =(-­૒4) n =a n d) 2*(-­૒4) n +3=a n =(-­૒3)*(2*(-­૒4) n-­૒1 +3)+4*(2*(-­૒4) n-­૒2 +3)=-­૒6*(-­૒4) n-­૒1 +8*(-­૒4) n-­૒2 +3=3+2*(-­૒ 4) n =a n Problem 3. a) r 2 -­૒r-­૒6=0 => r 1 =3, r 2 =-­૒2, m 1 =1, m 2 =1 a n = ɲ 1 r 1 n + ɲ 2 r 2 n = ɲ 1 3 n + ɲ 2 (-­૒2) n ɲ 1 =12/5, ɲ 2 =3/5 a n =(12/5)*3 n +(3/5)*(-­૒2) n b) r 2 -­૒7r+10=0 => r 1 =2, r 2 =5, m 1 =1, m 2 =1 a n = ɲ 1 *2 n + ɲ 2 *5 n ɲ 1 =3, ɲ 2 =-­૒1 a n =3*2 n -­૒5 n c) r 2 -­૒6r+8=0 => r 1 =2, r 2 =4, m 1 =1, m 2 =1 a n = ɲ 1 *2 n + ɲ 2 *4 n ɲ 1 =3, ɲ 2 =1 a n =3*2 n +4 n d) r 2 -­૒2r+1=0 => r 1 =1, m 1 =2 a

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hw8sol - SolutiontoHomework8 Problem1 a b c d e...

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