Difference between revisions of "1999 AHSME Problems/Problem 13"
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| − | Define a sequence of real numbers <math> a_1</math>, <math> a_2</math>, <math> a_3</math>, <math> \dots</math> by <math> a_1 | + | {{solution}} |
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| + | ==Problem== | ||
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| + | Define a sequence of real numbers <math> a_1</math>, <math> a_2</math>, <math> a_3</math>, <math> \dots</math> by <math> a_1 = 1</math> and <math> a_{n\plus{}1}^3 = 99a_n^3</math> for all <math> n \geq 1</math>. Then <math> a_{100}</math> equals | ||
<math> \textbf{(A)}\ 33^{33} \qquad | <math> \textbf{(A)}\ 33^{33} \qquad | ||
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\textbf{(D)}\ 99^{99} \qquad | \textbf{(D)}\ 99^{99} \qquad | ||
\textbf{(E)}\ \text{none of these}</math> | \textbf{(E)}\ \text{none of these}</math> | ||
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| + | ==See Also== | ||
| + | |||
| + | {{AHSME box|year=1999|num-b=12|num-a=14}} | ||
Revision as of 20:34, 2 June 2011
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Problem
Define a sequence of real numbers 
, 
, 
, 
by 
and $a_{n\plus{}1}^3 = 99a_n^3$ (Error compiling LaTeX. Unknown error_msg) for all 
. Then 
equals
See Also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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 | ||
