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  • 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

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

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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] imes number of term

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

 

Posted by

Deependra Verma

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