2009 AMC 8 Problems/Problem 5

Problem

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: $1\plus{}2\plus{}3\equal{}6$ (Error compiling LaTeX. Unknown error_msg). 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?

$\textbf{(A)}\ 11 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 37 \qquad \textbf{(D)}\ 68 \qquad \textbf{(E)}\ 99$

Solution

List them out, adding the three previous numbers to get the next number,

$1,2,3,6,11,20,37,\boxed{\textbf{(D)}\ 68}$

2009 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2009 AMC 8 Problems/Problem 5

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