SOLUTION: 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

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?
----------------------
The 1st, 3rd, 5th, etc sequences have the order 2,3,5
The 2nd, 4th, 6th, etc sequences have the order 5,3,2
----------------------
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".
---------------
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".
----
The sum of the squares is 3^2 + 2^2 = 13
============================================
Cheers,
Stan H.
RELATED QUESTIONS
What are the three next terms in the sequence, 1, 1, 2, 3,... (answered by htmentor,ikleyn)

What are the next three terms in the sequence... (answered by josgarithmetic,ikleyn,greenestamps)

1;3;5 are the first three terms of the first difference of a quadratic sequence. the 7th... (answered by greenestamps)

1 3 5 are the first three terms of the first differences of a quadratic sequence. The 7th (answered by KMST)

What are the first four terms of the sequence represented by the expression: n(n-2)-3 (answered by Fombitz)

The first two terms of the sequence are 2 and 5 what are the next TWO terms... (answered by josgarithmetic)

IF 3(5/9) AND 40(1/2) ARE THE FIRST AND THE LAST TERMS RESPECTIVELY, OF A GEOMETRIC... (answered by KMST)

For the arithmetic sequence 2,3,5 Please help me to prove that none of the terms are... (answered by greenestamps)

the first two terms of a sequence are 4 and 5, and each subsequent term is the sum of the (answered by Edwin McCravy)