Difference between revisions of "2000 AMC 10 Problems/Problem 6"
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==Problem== | ==Problem== | ||
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| + | The Fibonacci sequence <math>1, 1, 2, 3, 5, 8, 13, 21, \ldots</math> starts with two <math>1</math>s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence? | ||
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| + | <math>\mathrm{(A)}\ 0 \qquad\mathrm{(B)}\ 4 \qquad\mathrm{(C)}\ 6 \qquad\mathrm{(D)}\ 7\qquad\mathrm{(E)}\ 9</math> | ||
==Solution== | ==Solution== | ||
Revision as of 21:34, 8 January 2009
Problem
The Fibonacci sequence 
starts with two 
s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?
Solution
The pattern of the units digits are
In order of appearance:
.
is the last.
See Also
| 2000 AMC 10 (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 | ||
| All AMC 10 Problems and Solutions | ||
