Solve the following recurrence relation: a) an+1=dan+c, a0=0 b) an+13=2an3, a0=5 c) Fn=5Fn−1−6Fn−2, F0=1 and

babeeb0oL

babeeb0oL

Answered

2021-07-30

Solve the following recurrence relation:
a) an+1=dan+c, a0=0
b) an+13=2an3, a0=5
c) Fn=5Fn16Fn2, F0=1 and F1=4

Answer & Explanation

Nathaniel Kramer

Nathaniel Kramer

Expert

2021-07-31Added 78 answers

Step 1
According to the given information, it is required to solve the recurrence relation.
a) an+1=dan+c, a0=0
a0+1=a1=da0+ca1=c
a1+1=a2=da1+ca2=dc+c=(d+1)c
a2+1=a3=da2+ca3=d(dc+c)+ca3=d2c+dc+c=(d2+d+1)c
a3+1=a4=da3+ca4=d(d2c+dc+c)+ca4=(d3+d2+d+1)c
an=(dn+dn1+dn2++d+1)c
Step 2
b) an+13=2an3, a0=5
a0+13=a13=2a03a13=2(5)3=21(5)3
a1+13=a23=2a13a23=2×2(5)3=22(5)3
a2+13=a33=2a23a33=2×2×2(5)3=23(5)3

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