MathDB
Sequence of Numbers

Source:

November 26, 2009

Problem Statement

A sequence of numbers starts with 1 1, 2 2, and 3 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. 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? <spanclass=latexbold>(A)</span> 11<spanclass=latexbold>(B)</span> 20<spanclass=latexbold>(C)</span> 37<spanclass=latexbold>(D)</span> 68<spanclass=latexbold>(E)</span> 99 <span class='latex-bold'>(A)</span>\ 11 \qquad <span class='latex-bold'>(B)</span>\ 20 \qquad <span class='latex-bold'>(C)</span>\ 37 \qquad <span class='latex-bold'>(D)</span>\ 68 \qquad <span class='latex-bold'>(E)</span>\ 99