1,-3,2,-4,3,-5.... upto 2000 terms. find the average

• ((1-3)+(2-4)+(3-5)+...2000 terms)/2000 => (-2-2-2... 1000 terms)/2000 => -2000/2000=>-1
• 10 years agoHelpfull: Yes(36) No(1)
• here in the question the average is asked for up to 2000 terms.
  so up to 2000 terms will be
  
  {1,-3,2,-4,3,-5,.........,1000,-1002}
  
  so if we add them like this
  {(1-3)+(2-4)+(3-5)+.........+(1000-1002)}
  this will a sum of
  {-2-2-2-2-......-2} for thousand times
  i.e. {1000*(-2)}
  therefore the sum is -2000
  the average will be -2000/2000 = -1
• 10 years agoHelpfull: Yes(7) No(1)
• it is one of the ques in the today's tcs off campus.
• 10 years agoHelpfull: Yes(2) No(0)
• todays tcs question. options was 1,-1,2,-2
• 10 years agoHelpfull: Yes(2) No(1)
• ans is -1.
  1-3=-2 2-4=-2 3-5=-2 .hence there are total of 1000 (-2s) when the no. of terms is 2000 so the avg. will be {1000*(-2)}/2000=-1
• 9 years agoHelpfull: Yes(2) No(0)
• 1,2,3.....1000terms+-3,-4,-5......1000term
  S(n)=n/2(2*a+(n-1)d)
  1000/2(1*2+(1000-1)1)+1000/2(2(-3)+(1000-1)-1)
  =-2000
  hence,avg=-2000/2000=-1
• 9 years agoHelpfull: Yes(1) No(0)
• @PU the question is asking that upto 2000
  so the last three terms should be 1999 -2001 2000
  so i think we have to consider -2001 also
  this is because see in the question if the series ends on 3 then the previous number is -4 so if the series will end on 2000 then the previous number should be -2001
  and after that we have to find the ans..
• 10 years agoHelpfull: Yes(0) No(2)
• consider 1,2,3...2000 series;-3,-4,-5 ...-2002 series ;these two series are arthematic series so
  (1+2000)/2=1000.5
  (-3-2002)/2=-1002.5
  so (1000.5-1002.5)/2 =>-2/2=-1
  
• 9 years agoHelpfull: Yes(0) No(0)
• (1-3)+(2-4)....difference is -2
  so by 2000-2 = 1198
  so that (1, -3, 2 , ...2000,-2002)
  (1-2002)/2000=-1
• 9 years agoHelpfull: Yes(0) No(0)
• cross verify for 4 and 6 terms
  1-3+2-4=-4/4=-1
  (1-3+2-4+3-5)/6=-1
• 9 years agoHelpfull: Yes(0) No(0)
• ((1-3)+(2-4)+(3-5)+....till 2000terms)/2000
  =(-2-2-2....till 1000terms )/2000
  =-2000/2000
  =-1 ans
• 9 years agoHelpfull: Yes(0) No(0)
• as the difference is 2 between two terms there are 1000 terms if we conside r two ata atime
  -2*1000/2000=-1
• 9 years agoHelpfull: Yes(0) No(0)
• first take an average of th follow digits=(1-3+2-4+3-5) then result is=-6
  now take average is (1-3+2-4+3-5)/6=-6/6= -1 ans
• 9 years agoHelpfull: Yes(0) No(0)
• -2*1000/2000=-1
• 6 years agoHelpfull: Yes(0) No(0)