Difference between revisions of "1990 AHSME Problems/Problem 30"

Revision as of 01:00, 29 September 2014

If $R_n=\frac{1}{2}(a^n+b^n)$ where $a=3+2\sqrt{2}$ and $b=3-2\sqrt{2}$ , and $n=0,1,2,\cdots,$ then $R_{12345}$ is an integer. Its units digit is

$\text{(A) } 1\quad \text{(B) } 3\quad \text{(C) } 5\quad \text{(D) } 7\quad \text{(E) } 9$

$\fbox{E}$

1990 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 29	Followed by Problem 30
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

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-Let <math>R_n=\frac{1}{2}(a^n+b^n)</math> for each non-negative integer <math>n</math> where <math>a=3+2\sqrt{2}</math> and <math>b=3-2\sqrt{2}</math>. The value of <math>R_{12345}</math> is an integer. What is its units digit?
+== Problem ==
+If <math>R_n=\frac{1}{2}(a^n+b^n)</math>  where <math>a=3+2\sqrt{2}</math> and <math>b=3-2\sqrt{2}</math>, and <math>n=0,1,2,\cdots,</math> then <math>R_{12345}</math> is an integer.  Its units digit is
+<math>\text{(A) } 1\quad
+\text{(B) } 3\quad
+\text{(C) } 5\quad
+\text{(D) } 7\quad
+\text{(E) } 9</math>
+== Solution ==
+<math>\fbox{E}</math>
+== See also ==
+{{AHSME box|year=1990|num-b=29|num-a=30}}
+[[Category: Intermediate Algebra Problems]]
 {{MAA Notice}}