[Deleted because poster did not cite author.]

(100 + 150)/2=125 Mult 125*51(sum of #of terms +1)=6375

125-150/2=137.5, then 137.5*26=3575

6375-3575=2800

100+124/2=112, then 112*25=2800

I am just learning this too but i hope it helps!

The sum of the consecutive integers from 100 to 150 can be written as

(100)+(100+1)+(100+2)....(100+50)


The sum of the consecutive integers from 125 to 150 can be written as

(125)+(125+1)+(125+2)...(125+5)


We know that the 125 is the same as (100+25) so when you subtract the terms you will cross out everything after this entry to see whats left.


(100+25)+(100+26)......(100+50) Subtract (125)+(125+1)....(125+25)


All that you will have left over is:

(100)+(100+1)+(100+2)....(100+24) because we crossed out everything equal to 125 and everything after it.


Therefore it is equal to the sum of the consecutive integers from 100 to 124.

please cite the author of the problem; otherwise it will be deleted. Thanks!