Difference between revisions of "1994 AHSME Problems/Problem 6"
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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> d+0=1\implies d=1</cmath> | ||
| + | <cmath>c+1=0\implies c=-1</cmath> | ||
| + | <cmath> b+(-1)=1\implies b=2</cmath> | ||
| + | <cmath>a+2=-1\implies a=\boxed{\textbf{(A)}-3.}</cmath> | ||
| + | |||
| + | --Solution by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=200685 TheMaskedMagician] | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AHSME box|year=1994|num-b=5|num-a=7}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 17:27, 9 January 2021
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 .
![\[d+0=1\implies d=1\]](http://latex.artofproblemsolving.com/9/c/7/9c724e486f574487b2413594589cfb1a73d8a632.png)
![\[c+1=0\implies c=-1\]](http://latex.artofproblemsolving.com/a/4/9/a499bb1932a96cd062ebfa9e1fa6f9b0bd3f502f.png)
![\[b+(-1)=1\implies b=2\]](http://latex.artofproblemsolving.com/3/7/6/37674399b748d7e4b60e93a9790d9169e56121d8.png)
![\[a+2=-1\implies a=\boxed{\textbf{(A)}-3.}\]](http://latex.artofproblemsolving.com/6/e/c/6ecfa8e3b9d5460463735971957381c83183ff10.png)
--Solution by TheMaskedMagician
See Also
| 1994 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
