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The Problem of the Third Week
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Continue the sequence:

          178, 177, 175, 169, 145,....
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the difference between 178 and 177 is 1,
and the difference between  177 and 175 is 2, but the difference between 175 and 169 is 6, and the difference between 169 and 145 is 24, so as we can realize, it is a sequence,
(1),
(1).(2)=2,
(1).(2).(3)=6, 
(1).(2).(3).(4)=24.

From this, it is so easy to see that the next difference should be

(1).(2).(3).(4).(5)=120.

By subtracting 120 from 145, we get 25, which is the next number.
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