1-2+3-4+.............-200 find the avg of these 200 terms

• There are two series.
  1st [1+3+5+..........199] this gives 100 terms.
  Sum of this series= 100/2(1+199)=10000
  2nd series -[2+4+6+.....200]
  sum= -100/2(2+200) =-10100
  
  So sum of series =10000-10100=-100
  
  Hence average = -100/200= -1/2
• 8 years agoHelpfull: Yes(15) No(0)
• -1/2
  
  Divide the terms in a series as 1+3+5+7+....+199 and -2 -4 -6 -8 - ......-20
  As there are 100 terms in each series. Finding the sum of 1st & 2nd series
  =(100/2)[2*1 + (100-1)*2] + (100/2)[2*-2 +(100-1)*-2]
  =50*200+50*(-202)=-100
  So average=-100/200= -1/2
• 8 years agoHelpfull: Yes(4) No(0)
• (1-2)=-1
  (3-4)=-1
  (5-6)=-1
  ...........all these terms upto +199-200 will be -1 .since we grouped the nos into 2 the total no of numbers in the series becomes 200/2=100
  Now,summation of -1 ,100 times gives=-1*100=-100
  Therefore,average of the 200 terms ,-100/200= -2
  
• 8 years agoHelpfull: Yes(1) No(1)
• 99.5
  1,3,5.....199 = 1+(100-1)*2, -2-4-6....-200 = -( 2+(100-1)*2. The difference is -1. Hence Average should be 0.5 less i.e 99.5
• 8 years agoHelpfull: Yes(1) No(0)
• Let n=200
  avg of consecutive odd numbers=n
  avg of consecutive even no=n+1
  Since avg of odd and even numbers has to be found we can do
  avg =(200-201)/2=-1/2
• 8 years agoHelpfull: Yes(1) No(0)
• Let n=200
  avg of consecutive odd numbers=n
  avg of consecutive even no=n+1
  Since avg of odd and even numbers has to be found we can do
  avg =(200-201)/2=-1/2
• 8 years agoHelpfull: Yes(0) No(0)