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Mathematics-Online problems:
Problem of the week
For a sequence
let each term be
less than the sum of its two neighbors:
Every such sequence is periodic.
Determine the length of the period.
Compute the sum of the first 66 terms of the sequence.
Find the terms
and
of the sequence with
.
Hint:
A sequence is called periodic if
for
and some
. The smallest
having this property is called the length of the period of that sequence.
Answer:
Length of the period:
Sum:
Terms of sequence:
[
solution to the problem of the previous week
]