SOLUTION: How much less is the sum of all odd digits between 24 and 308 than the sum of all even digits between 23 and 307?

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Question 411258:
How much less is the sum of all odd digits between 24 and 308 than the sum of all even digits between 23 and 307?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

How much 'less' is the sum of all odd digits 'between' 24 and 308 

than the sum of all even digits 'between' 23 and 307?

a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad

  306 = 26 + (n-1)2

  306 = 26 + 2n - 2

   282 = 2n

    n = 141

S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29

S%5B141%5D=%28141%2F2%29%28+52+%2B+%28140%292%29  

S%5B141%5D=%28141%2F2%29%28332%29 = 23,406    |sum of evens



305 = 25 + 2n-2

 141 = n

 141/2(50 + 280) = 141/2*330 = 23,265  |sum of odds



    23,406 - 23,265 = 141