SOLUTION: Find the following four terms of the sequence given the following recursive formula: a(1)=8 a(2)=-3 and a(n)=2a(n-1)+a(n-2) for n≥3

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Question 765187: Find the following four terms of the sequence given the following recursive formula:
a(1)=8 a(2)=-3 and a(n)=2a(n-1)+a(n-2) for n≥3
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

a(n) = 2a(n-1)+a(n-2)  for n≥3

a(1) = 8
a(2) = -3
a(3) = 2a(3-1)+a(3-2) = 2a(2)+a(1) = 2(-3)+8 = -6+8 = 2
a(4) = 2a(4-1)+a(4-2) = 2a(3)+a(2) = 2(2)+(-3) = 4-3 = 1
a(5) = 2a(5-1)+a(5-2) = 2a(4)+a(3) = 2(1)+2 = 2+2 = 4
a(6) = 2a(6-1)+a(6-2) = 2a(5)+a(4) = 2(4)+1 = 8+1 = 9
a(7) = 2a(7-1)+a(7-2) = 2a(6)+a(5) = 2(9)+4 = 18+4 = 22
a(8) = 2a(8-1)+a(8-2) = 2a(7)+a(6) = 2(22)+9 = 44+9 = 53
a(9) = 2a(9-1)+a(9-2) = 2a(8)+a(7) = 2(53)+22 = 106+22 = 128
a(10) = 2a(10-1)+a(10-2) = 2a(9)+a(8) = 2(128)+53 = 256+53 = 309

Edwin
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