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aleksklad [387]
3 years ago
14

What are the first three terms of the sequence defined by the recursive function an=an-1-(an-2-4), when a5=-2 and a6=0

Mathematics
1 answer:
BaLLatris [955]3 years ago
4 0

Answer:

6, 10, 8

Step-by-step explanation:

aₙ= aₙ₋₁ - (aₙ₋₂ - 4)= aₙ₋₁ - aₙ₋₂ + 4

a₅= -2

a₆= 0

-----------

aₙ₋₂= aₙ₋₁ - aₙ + 4

  • a₄= a₅- a₆ + 4 = -2 - 0 + 4 = 2
  • a₃= a₄ - a₅ + 4 = 2 - (-2) + 4 = 8
  • a₂= a₃ - a₄ + 4 = 8 - 2 + 4 = 10
  • a₁= a₂ - a₃ + 4 = 10 - 8 + 4 = 6

The first 3 terms: 6, 10 and 8

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F(1) = 160 is given to us. We'll use it to find f(2)
f(n+1) = -2*f(n)
f(1+1) = -2*f(1) ... replace every n with 1
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Now use f(2) to find f(3)
f(n+1) = -2*f(n)
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f(n+1) = -2*f(n)
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f(4) = -2*640 ... replace f(3) with 640
f(4) = -1280

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