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2009 AMC 8 Question 5

AMC8 · 2009 AMC 8

Question 5

A sequence of numbers starts with $1,$ $2,$ and $3.$ The fourth number of the sequence is the sum of the previous three numbers in the sequence: $1 + 2 + 3 = 6.$ In the same way, every number after the fourth is the sum of the previous three numbers. What is the eighth number in the sequence?
  1. $11$
  2. $20$
  3. $37$
  4. $68$
  5. $99$