1994 AHSME Problems/Problem 6

Revision as of 14:17, 28 June 2014 by TheMaskedMagician (talk | contribs) (Solution)

Problem

In the sequence \[..., a, b, c, d, 0, 1, 1, 2, 3, 5, 8,...\] each term is the sum of the two terms to its left. Find $a$.

$\textbf{(A)}\ -3 \qquad\textbf{(B)}\ -1 \qquad\textbf{(C)}\ 0 \qquad\textbf{(D)}\ 1 \qquad\textbf{(E)}\ 3$

Solution

We work backwards to find $a$.

\begin{align*}d+0=1&\implies d=1\\ c+1=0&\implies c=-1\\ b+(-1)=1&\implies b=2\\ a+2=-1&\implies a=\boxed{\textbf{(A) }-3.} (Error compiling LaTeX. Unknown error_msg)

--Solution by TheMaskedMagician