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Find the generating function for the sequence given recursively by
an - 2an-1 - 4an-2 = 0 with a0 = 2 and a1 = 5?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find the generating function for the sequence given recursively byan -...
an - 2an-1 - 4an-2 = 0
an = 2an-1 + 4an-2 (given)
a0 = 2, a1 = 5
a2 = 2(5) + 4(2) = 18, a= 2(18) + 4(5) = 56
a4 = 2(56) + 4(18) = 184
∴ sequence: 2, 5, 18, 56, 184
G(x) = 2 + 5x + 18x2 + 56x3 + 184x4 …
2xG(x) = 4x + 10x2 + 36x3 + 112x4 …
4x2G(x) = 8 x2 + 20x3 + 72x4 …
G(x)(1 – 2x – 4x2) = 2 + x
G(x) = 
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Most Upvoted Answer
Find the generating function for the sequence given recursively byan -...
an - 2an-1 - 4an-2 = 0
an = 2an-1 + 4an-2 (given)
a0 = 2, a1 = 5
a2 = 2(5) + 4(2) = 18, a= 2(18) + 4(5) = 56
a4 = 2(56) + 4(18) = 184
∴ sequence: 2, 5, 18, 56, 184
G(x) = 2 + 5x + 18x2 + 56x3 + 184x4 …
2xG(x) = 4x + 10x2 + 36x3 + 112x4 …
4x2G(x) = 8 x2 + 20x3 + 72x4 …
G(x)(1 – 2x – 4x2) = 2 + x
G(x) = 
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Find the generating function for the sequence given recursively byan - 2an-1 - 4an-2 = 0 with a0 = 2 and a1 = 5?a)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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