| Arithmetic Sequences |
Consider all increasing arithmetic sequences with common difference 1, {t1,t2,t3...}. If the absolute difference of
and
is 1100, find the sum of all possible values of
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Problem Moderated by: Douglas |
| Problem Solution |
Let t1 = a
tn = a + (n-1)
t2 = a + 1
t4 = a + 3
t100 = a+99
(a+(a+99))100/2 = 50(2a+99)
((a+1)+(a+99))50/2 = 25(2a+100)
|50(2a+99)-25(2a+100)| = |50(a+49)|=1100
a + 49 = 22 or -22
a = -27 or -71
((a+3)+(a+99))25/2 = 25(a+51) = 600 or -500
600 - 500 = 100 |
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