Question

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

Answer 1

6, 10, 8

Explanation:

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

a₅= -2

a₆= 0

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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