Difference between revisions of "1992 AIME Problems/Problem 8"
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== Problem == | == Problem == | ||
| − | For any sequence of real numbers <math>A=(a_1,a_2,a_3,\ldots)</math>, define <math>\Delta A</math> to be the sequence <math>(a_2-a_1,a_3-a_2,a_4-a_3,\ldots)</math>, whose <math>n^\mbox{th}_{}</math> term is <math>a_{n+1}-a_n^{}</math>. Suppose that all of the terms of thet sequence <math>\Delta(\Delta A^{}_{})</math> are <math>1^{}_{}</math>, and that <math>a_{19}=a_{92}^{}=0</math>. Find <math>a_1^{}</math>. | + | For any sequence of real numbers <math>A=(a_1,a_2,a_3,\ldots)</math>, define <math>\Delta A^{}_{}</math> to be the sequence <math>(a_2-a_1,a_3-a_2,a_4-a_3,\ldots)</math>, whose <math>n^\mbox{th}_{}</math> term is <math>a_{n+1}-a_n^{}</math>. Suppose that all of the terms of thet sequence <math>\Delta(\Delta A^{}_{})</math> are <math>1^{}_{}</math>, and that <math>a_{19}=a_{92}^{}=0</math>. Find <math>a_1^{}</math>. |
== Solution == | == Solution == | ||
Revision as of 22:50, 10 March 2007
Problem
For any sequence of real numbers 
, define 
to be the sequence 
, whose $n^\mbox{th}_{}$ (Error compiling LaTeX. Unknown error_msg) term is 
. Suppose that all of the terms of thet sequence 
are 
, and that 
. Find 
.
Solution
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