The sequence repeats with a cycle of 10, the first 10 elements are:
1607, 1707, 1814, 1914, 200, -1607, -1707, -1814, -1914, -200
So element 100 is the same as element 0 which is 1607
Consider labelling the elements of the sequence: a,b,c,d,e,f,g,...
a is the 0-th element and k is the 10th.
Each element is the opposite of the one 5 places before.
e = d-c+b-a
f = (d-c+b-a) -d+c-b = -a
g = (-a) - (d-c+b-a) + d - c = -b
h = (-b) - (-a) + (d-c+b-a) - (d) = -c
i = (-c) - (-b) + (-a) - (d-c+b-a) = -d
j = (-d) - (-c) + (-b) - (-a) = -e
k = (-e) - (-d) + (-c) - (-b) = -f = a
etc
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Posted by Larry
on 2024-07-11 11:13:52 |
Solution
