# The sum of the even numbers between 1 and k is 79*80, where k is an odd number, then k=?(A) 79(B) 80(C) 81(D) 157(E) 159

Solution: As k is odd then the last even  number   between 1 and k will be k-1 and the first even number will be 2.

So , there are

$\\\Rightarrow [(k-1)-2]/2 +1=(k-1)/2 \\ \\$ Even number between 1 and k.

Next , the sum of the elements in any evenly spaced set is given by:

$\\ sum=[(first+last)/2]\times$ number of term

$\\\Rightarrow [(2+k-1)/2]\times (k-1)/2=79*80\\ \\\Rightarrow (k-1)(k+1)=158*160\\ \\\Rightarrow k=159Ans$

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