1975 AHSME Problems/Problem 15
Revision as of 22:41, 24 June 2019 by Someonenumber011 (talk | contribs) (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...")
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
2019 AHSME (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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.