SOLUTION: 2+4+6+...+34 ----------- - = ? 3+6+9+...+51 In this problem, instead of adding the numbers one by one is there any short method? Thank you.

Question 52995: 2+4+6+...+34
------------- = ?
3+6+9+...+51
In this problem, instead of adding the numbers one by one is there any short method?
Thank you.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
2+4+6+...+34
------------- = ?
3+6+9+...+51
In this problem, instead of adding the numbers one by one is there any short method?
these are called arithmatic serties when difference between 2 consecutive numbers is constant..here 4-2=6-4=2....=34-32
there is formula to find the sum in such cases.but if you are not taught that there is a simple trick you cn use.
we have to find
s=2 + 4 + 6+8+.........+30+32+34........now write them in reverse order
s=34+32 +30+28+........+6 + 4 +2........now add
-----------------------------------------------------
2s=36+36+36+36+........+36+36+36=36*17 times
s=36*17/2=306
i think you can now do the second problem by your self
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