Question 976324: If the series {ak} satisfies a1=1, a2=2, and (ak)-4(ak-1)+3(ak-2)=0 for K greater than or equal to 3, then ak=(1+p)/q for k greater than or equal to 1. Find p and q.
Please use the below representation-
ak = kth term = a subscript k
a1 = 1st term = a subscript 1
a2 = 2nd term = a subscript 2
ak-1 = (k-1)th term = a subscript k-1
ak-2 = (k-2)th term = a subscript k-2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If the series {ak} satisfies a1=1, a2=2, and (ak)-4(ak-1)+3(ak-2)=0 for K greater than or equal to 3, then ak=(1+p)/q for k greater than or equal to 1. Find p and q.
Please use the below representation-
ak = kth term = a subscript k
a1 = 1st term = a subscript 1
a2 = 2nd term = a subscript 2
ak-1 = (k-1)th term = a subscript k-1
ak-2 = (k-2)th term = a subscript k-2
------
a(3) - 4*a(2) + 3*a(1) = 0
---
a(3) - 4*2 + 3*1 = 0
---
a(3) - 8 + 3 = 0
a(3) = 5
------------
ak=(1+p)/q
Therefore::
a(3) = (1+p)/q = 5/1
------
1+p = 5, so p = 4
q = 1
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Cheers,
Stan H.
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