Difference between revisions of "1975 AHSME Problems/Problem 15"
(Created page with "==Problem== In the sequence of numbers <math>1, 3, 2, \ldots</math> each term after the first two is equal to the term preceding it minus the term preceding that. The sum of t...") |
(→See Also) |
||
| Line 11: | Line 11: | ||
==See Also== | ==See Also== | ||
| − | {{AHSME box|year= | + | {{AHSME box|year=1975|ab=A|num-b=14|num-a=16}} |
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 22:42, 24 June 2019
Problem
In the sequence of numbers 
each term after the first two is equal to the term preceding it minus the term preceding that. The sum of the first one hundred terms of the sequence is
Solution
First, write a few terms of the sequence:
Notice how the pattern repeats every six terms and every six terms have a sum of 0. Then, find that the 
th term is 
and the sum of the all those previous terms is 
. Then, write the 97th to the 100th terms down: 
and add them up to get the sum of 
See Also
| 1975 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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. 
