We have a series where the sum of any 7 consecutive terms is negative and the sum of any 11 consecutive terms is positive. What is the maximum number of terms in this series?
(In reply to
Tightening the range by Brian Smith)
14 terms is indeed maximum.
I used the designation in the problem where the sum of any 7 consecutive terms is negative and the sum of any 11 consecutive terms is positive. I'll write the first and last terms of a series in parentheses to indicate sum. Then it's just a matter of checking the series left to right.
(1-7) is negative, (1-11) is positive, so (8-11) is positive.
(2-8) is negative, (2-12) is positive, so (9-12) is positive.
(3-9) is negative, (3-13) is positive, so (10-13) is positive.
(4-10) is negative, (4-14) is positive, so (11-14) is positive.
(5-11) is negative, (5-15) is positive, so (12-15) is positive.
The first and last lines imply (8-15) is positive but that's 8 terms, one too many.
|
|
Posted by xdog
on 2019-06-18 22:37:47 |
re: Tightening the range
