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# The sum of the even numbers between 1 and n is 79*80, where

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Intern
Joined: 22 Feb 2017
Posts: 19
Location: India
GPA: 3.6
WE: Engineering (Manufacturing)
Re: The sum of the even numbers between 1 and n is 79*80, where  [#permalink]

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18 Nov 2018, 22:22
chan4312 wrote:
The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

(A) 79
(B) 80
(C) 81
(D) 157
(E) 159

Clearly, this is an arithmetic progression with the 1st term being '2' and last term being '(n-1)' OR 'k'(say) ;

So, sum of the progression as per formulae, S= k/2*[2a+{k-1}*d]=79*80 [Where, k=last term & d=common difference & a=1st term] ;

=>k/2*[2*2+{k-1}*2]=79*80 =>k= 79 OR -80 =>k=79 ;

Formula for 'k' th term in an arithmetic progression= [a + (k-1)*d]=[2+(79-1)*2]=158 ;

Since, k=(n-1) =>n=158+1=159 and thus the answer choice is 'E' ;
Re: The sum of the even numbers between 1 and n is 79*80, where &nbs [#permalink] 18 Nov 2018, 22:22

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