consider the sequence 1,-2,3,-4,5,-6 .what is the average of the first 200 terms of the sequence?

• ave = (1-2)+(3-4)+(5-6)+.....+(199-200) / 200
  
  = (-1)+(-1)+(-1)+..... 100 times / 200
  
  = -100/200
  = -1/2
  = -0.5
  
• 10 years agoHelpfull: Yes(18) No(0)
• 1+3+5+7+.....+199
  tot=100/2(1+199)=100*100=10000
  -2 -4 -6 -8.....-200
  total=100/2 (-2-200)= 100*(-101)=-10100
  avg= -100/200 = -0.5
• 10 years agoHelpfull: Yes(3) No(0)
• sum of odd 100 terms 1,3,5... 199
  = (100/2)(1+199) = 10000
  sum of even 100 terms -2,-4,-6......-200
  =(100/2)(-2-200) = 10100
  avg of 200 terms = (10000 - 10100)/200
  = -0.5
• 10 years agoHelpfull: Yes(1) No(0)
• 1-2=-1 , 3-4=-1 , in the same way group total no in 100 equal parts . the value of total is 100*(-1) = -100. total group is 100 so that average is -100/100=-1 . hence -1 is final ans.
• 10 years agoHelpfull: Yes(1) No(2)
• Ans: -1/2
  
  Given that 1,-2,3,-4,5,-6.........200
  Divide it into
  1. 1,3,5,7,9..........199 (odd numbers)
  2. -(2,4,6,8,10.......200). (even numbers)
  
  Avg=>((100/2(1+199)) - (100/2(2+200)))/200
  
  = (50(200-202))/200
  
  =-1/2.
  
  
• 10 years agoHelpfull: Yes(1) No(0)
• ans is -1/2
• 10 years agoHelpfull: Yes(1) No(0)
• -0.5
  a pattern is forming of even no. and odd no.
• 10 years agoHelpfull: Yes(0) No(0)
• it will be -0.5
• 10 years agoHelpfull: Yes(0) No(0)
• Sum of the numbers from 1-2...100 = -50
  Similarly 101-102....200 = -50
  -50-50 = -100
  -100/200 = -0.5
• 10 years agoHelpfull: Yes(0) No(0)