2013 AMC 12A Problems/Problem 14
Problem
The sequence
, , , ,
is an arithmetic progression. What is ?
Solution 1
Since the sequence is arithmetic,
+ = , where is the common difference.
Therefore,
= - = , and
= () =
Now that we found , we just add it to the first term to find :
+ =
= = = = , which is
Solution 2
As the sequence , , , , is an arithmetic progression, the sequence must be a geometric progression.
If we factor the two known terms we get and , thus the quotient is obviously and therefore .
Video Solution by OmegaLearn
https://youtu.be/RdIIEhsbZKw?t=944
~ pi_is_3.14
See also
2013 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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All AMC 12 Problems and Solutions |
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