Difference between revisions of "1994 AHSME Problems/Problem 6"
(Created page with "==Problem== In the sequence <cmath> ..., a, b, c, d, 0, 1, 1, 2, 3, 5, 8,... </cmath> each term is the sum of the two terms to its left. Find <math>a</math>. <math> \textbf{(A)}...") |
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<math> \textbf{(A)}\ -3 \qquad\textbf{(B)}\ -1 \qquad\textbf{(C)}\ 0 \qquad\textbf{(D)}\ 1 \qquad\textbf{(E)}\ 3 </math> | <math> \textbf{(A)}\ -3 \qquad\textbf{(B)}\ -1 \qquad\textbf{(C)}\ 0 \qquad\textbf{(D)}\ 1 \qquad\textbf{(E)}\ 3 </math> | ||
==Solution== | ==Solution== | ||
| + | We work backwards to find <math>a</math>. | ||
| + | |||
| + | <cmath>\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.}</cmath> | ||
| + | |||
| + | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | ||
Revision as of 15:17, 28 June 2014
Problem
In the sequence
![\[..., a, b, c, d, 0, 1, 1, 2, 3, 5, 8,...\]](http://latex.artofproblemsolving.com/d/d/b/ddb98ab5cb4c79e636eebd6161fcdfea100f7c3c.png)
each term is the sum of the two terms to its left. Find 
.
Solution
We work backwards to find .
\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
