Difference between revisions of "2023 AMC 10B Problems/Problem 6"
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On my copy of the AMC 10B, the order of the answers is different, so the correct answer is (E) 674 | On my copy of the AMC 10B, the order of the answers is different, so the correct answer is (E) 674 | ||
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==Solution 2== | ==Solution 2== | ||
Revision as of 18:49, 15 November 2023
Problem
Let 
, and 
for 
. How many terms in the sequence 
are even?
On my copy of the AMC 10B, the order of the answers is different, so the correct answer is (E) 674
Solution 2
Like in the other solution, we find a pattern, except in a more rigorous way.
Since we start with 
and 
, the next term is 
.
We start with odd, then odd, then (the sum of odd and odd) even, (the sum of odd and even) odd, and so on. Basically the pattern goes: odd, odd, even, odd odd, even, odd, odd even…
When we take 
we get 
with a remainder of one. So we have full cycles, and an extra odd at the end.
Therefore, there are 
evens.
~e_is_2.71828
