1,-2,3,-4,5...........what is the average of first 200 numbers?

• let us take first two numbers 1-2=-1
  3-4=-1
  5-6=-1
  7-8=-1
  9-10=-1
  like this for 10 numbers it is -5
  for 100 numbers it is -50
  for 200 numbers it is -100
  now the average is -100/200=-1/2=-0.5
  so the answr is -0.5
  
  
• 11 years agoHelpfull: Yes(45) No(0)
• sry, i have said the ans as the sum of numbers, if we want avg means...it is
  -100/200 = -1/2
• 11 years agoHelpfull: Yes(6) No(0)
• answer is -100....(1+3+5+7+------+199)-2(1+2+3+-------+100)....which is
  sum of first n odd numbers-2(sum of first n natural numbers)
  n^2-2[(n(n+1)/2)]
  = 100^2 - 2[100(101)/2]
  100(100-101) = -100...
• 11 years agoHelpfull: Yes(5) No(7)
• (1+3+5....+199)+(-2+(-4)+....(-200))
  sum of a.p. series when first nd last term known=a+l/2
  so 1+199/2=100
  -2+-200/2=-101
  now avg.=100+(-101)/2=-.5 ans.
• 11 years agoHelpfull: Yes(2) No(0)
• below methods are very good...it can also be solve by
  we can see that 100 terms formin a.p=1,3,5 there sum upto 100 terms=10000
  and other 100 terms -2,-4 ,there sum upto 100 terms=-10100
  so the avg=10000-10100/200=-100/200=-0.5
• 11 years agoHelpfull: Yes(1) No(0)