So short, yet so complete
The number of terms in an arithmetic progression is 2 0 1 5 . When the ratio of the sum of odd terms to the sum of even terms is expressed as N M , where M and N are coprime positive integers, what is the value of 2 N ?
Note for clarity: Odd terms indicate terms at "ODD" cardinality. Similarly for even terms.
The answer is 2014.
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3 solutions
01
Note: This is not a rigorous solution.
So the ratio is same regardless of the AP one chooses. That means any AP following all the demands of the question will give the ratio.
Let the AP be 1 , 1 , 1 . . . . . , 1 Now we're asked to find 2 N = 2• Sum of even terms
which is clearly 2 0 1 4
This question is not completely right.
For eg. : What if the A.P. is 2 , 2 , 2 , . . . . u p t o 2 0 1 5 t e r m s ??!!
Please modify it. @Krishna Ar
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Still it will be 1 0 0 7 1 0 0 8 . Check your thinking please.
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If all the terms are equal to 2 ,
then s u m o f e v e n n o . s u m o f o d d n o . = 4 0 3 0 0 = 0 ,
then how the answer will be 1 0 0 7 1 0 0 8 ????
Can you explain it ?
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@Sandeep Bhardwaj – Gosh! Its odd terms, not odd numbers!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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@Krishna Ar – You should mention it as "terms at odd places". Otherwise "odd terms" means the terms which are "odd". It doesn't surely verify at pointing the terms at odd places. Don't you think so !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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@Sandeep Bhardwaj – k ill do it
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@Krishna Ar – thank you dude. !
@Krishna Ar – u sound like "kill u" then "kill" then "k ill" :p
see this is really an easy one we could take an A.P. as 1 , 2 ,3 ,4 ,5 ,6 .............2015
then we can write the sum of all odd nos. as( 2015 +1) * 1008/2 and of even nos . as
(2014 +2) *1007/2 . the ratio of sum of odd / sum of even terms can be written as
504*2 / 1007 = 1008 / 1007 then, 1008 +1007 = 2015 and 1008 -1007 =1
therefore 2015 -1 = 2014
Non-Rigorous