Difference between revisions of "2000 AMC 12 Problems/Problem 4"

Revision as of 12:10, 13 November 2006

Problem

The Fibonacci sequence $1,1,2,3,5,8,13,21,\ldots$ starts with two 1s, 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?

$\mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 4 } \qquad \mathrm{(C) \ 6 } \qquad \mathrm{(D) \ 7 } \qquad \mathrm{(E) \ 9 }$

Solution

Looking at the Fibonacci Sequence in $\bmod{10}$ :

$1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,....$

The last digit to appear in the units position of a number in the Fibonacci sequence is $6 \Rightarrow C$ .

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Difference between revisions of "2000 AMC 12 Problems/Problem 4"

Revision as of 12:10, 13 November 2006

Problem

Solution

See also

Revision as of 18:23, 5 November 2006 (view source) Xantos C. Guin (talk \| contribs) (added category and link to previous and next problem) ← Older edit	Revision as of 12:10, 13 November 2006 (view source) JBL (talk \| contribs) m (2000 AMC 12/Problem 4 moved to 2000 AMC 12 Problems/Problem 4) Newer edit →
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