What is the average of the first 200 terms of the series
1, -2, 3, -4, 5, -6, 7 …………

• (1-2) + (3-4) + ...... 100 times
  
  (-1) + (-1) + (-1) + ....100 times
  
  average = (-100) / 200 = -1/2
• 8 years agoHelpfull: Yes(23) No(0)
• we can write
  1+3+5+7+9+11+13.........+199 i.e 100 terms and
  sum of n odd natural numbers is n^2 i.e 100^2 =10,000
  
  -(2+4+6+8+10+12...........+200) i.e 100 terms and
  sum of n even natural numbers is n(n+1) i.e -(100(100+1))= -10,100
  average of first 200 terms = (10,000+(-10,100))/200
  =-100/200
  =-1/2 Ans.
• 8 years agoHelpfull: Yes(3) No(1)
• (1-2+3-4...........-200)/200=(-100/200)=(-1/2)
• 8 years agoHelpfull: Yes(2) No(0)
• (1-2)/2+(3-4)/2+....... 100 terms
  =-1/2+(-1/2)+.....100 terms
  =-50
• 8 years agoHelpfull: Yes(1) No(5)
• 1,-2,3,-4,5,-6,7,-8,9,-10
• 8 years agoHelpfull: Yes(1) No(1)
• sum of 100 odd numbers till 1-199=10000
  sum of 100 even numbers till 2-200=10100
  now subtact 2 from 1,we get -100;
  so avg=-100/200=-0.5
• 8 years agoHelpfull: Yes(1) No(0)
• first find the sum of all (-)ve numbers i.e -2, -3, -4, -5,-6,-7, .............. -200
  there are totally 199 terms therefore n=199.
  so we get a1= -2, d=-1, an=-200.
  now sn= n(a1+an)/2 i.e sn = 199(-202)/2
  =-199(101) = -20099
  now add positive nuber to it so total is -20099=1 = 20098
  
  to get avg divide it by 200 so therefore 20098/200 = -100.49
  
  now the average of the given term is -100.49
• 8 years agoHelpfull: Yes(0) No(5)
• -100/200 = -1/2
• 8 years agoHelpfull: Yes(0) No(0)
• The series consists of odd and even terms as 1, 3, 5, ..., 99 and -2, -4, -6, ...., -100.
  So sum of the odd terms = 100/2*(1 + 99) [Sum of n terms of AP]
  Again, sum of the even terms = 100/2*(-2 -100) [Sum of n terms of AP]
  Total sum = 50*(100 -2 -100) = 50*(-2) = -100
  Hence average = -100/200 = -1/2
• 6 years agoHelpfull: Yes(0) No(0)