Question 280961: 2, 3, 5, 5, 3, 2, ...
The first three terms of the sequence are 2, 3, and 5. After that, subsequent terms are produced by switching the order of the previous three numbers. What is the sum of the squares of the 14th and 43rd terms?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 2, 3, 5, 5, 3, 2, ...
The first three terms of the sequence are 2, 3, and 5. After that, subsequent terms are produced by switching the order of the previous three numbers. What is the sum of the squares of the 14th and 43rd terms?
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The 1st, 3rd, 5th, etc sequences have the order 2,3,5
The 2nd, 4th, 6th, etc sequences have the order 5,3,2
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Procedure to find the 14th term:
Determine which sequence it is in.
14/3 = 4 + 2/3
So that term is in the 5th sequence which is 2,3,5
The 14th is the 2nd term in that sequence so it is "3".
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Similarly with the 43rd term:
43/3 = 14 1/3
So the 43rd is in the 15th sequence which is 2,3,5
It is the 1st term which is "2".
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The sum of the squares is 3^2 + 2^2 = 13
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Cheers,
Stan H.
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