2013 AMC 12A Problems/Problem 7: Difference between revisions
Epicwisdom (talk | contribs) Created page with "<math>S_9 = 110</math>, <math>S_7 = 42</math> <math>S_8 = S_9 - S_ 7 = 110 - 42 = 68</math> <math>S_6 = S_8 - S_7 = 68 - 42 = 26</math> <math>S_5 = S_7 - S_6 = 42 - 26 = 16</m..." |
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== Problem== | |||
The sequence <math>S_1, S_2, S_3, \cdots, S_{10}</math> has the property that every term beginning with the third is the sum of the previous two. That is, <cmath> S_n = S_{n-2} + S_{n-1} \text{ for } n \ge 3. </cmath> Suppose that <math>S_9 = 110</math> and <math>S_7 = 42</math>. What is <math>S_4</math>? | |||
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 12\qquad\textbf{(E)}\ 16\qquad </math> | |||
==Solution== | |||
<math>S_9 = 110</math>, <math>S_7 = 42</math> | <math>S_9 = 110</math>, <math>S_7 = 42</math> | ||
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<math>S_4 = S_6 - S_5 = 26 - 16 = 10</math> | <math>S_4 = S_6 - S_5 = 26 - 16 = 10</math> | ||
== See also == | |||
{{AMC12 box|year=2013|ab=A|num-b=6|num-a=8}} | |||
Revision as of 17:35, 22 February 2013
Problem
The sequence 
has the property that every term beginning with the third is the sum of the previous two. That is, ![\[S_n = S_{n-2} + S_{n-1} \text{ for } n \ge 3.\]](http://latex.artofproblemsolving.com/4/9/d/49d16ad7dec282dc9ee086290f9aa43ba22b0b78.png)
Suppose that 
and 
. What is 
?
Solution
,
See also
| 2013 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 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 12 Problems and Solutions | |
