SOLUTION: find the sum of even integers between 1 and 101 in a arithmetic sequence

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Question 1039512: find the sum of even integers between 1 and 101 in a arithmetic sequence
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of ALL the integers from 1 to n
is given by:
+S+=+%28+n%2A%28+n%2B1+%29%29+%2F+2+
If +n+=+101+,
+S+=+%28+101%2A102+%29+%2F+2+
+S+=+10302%2F2+=+5151+
------------------------
The sum of the ODD integers from 1 to n?
I notice that
+1+=+1+
+1+%2B+3+=+4+
+1+%2B+3+%2B+5+=+9+
+1+%2B+3+%2B+5+%2B+7+=+16+
Let +k+ = the number of odd integers from 1 to n
So, +S%5Bodd%5D+=+k%5E2+
The are +51+ odd integers in 1 - 101 sequence
+k%5E2+=+51%5E2+
+S%5Bodd%5D+=+2601+
-------------------
+S%5Beven%5D+=+S+-+S%5Bodd%5D+
+S%5Beven%5D+=+5151+-+2601+
+S%5Beven%5D+=+2550+
Hope I got it!