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

• 1-2=-1,3-4=-1,5-6=-1......then avg -(100)/200=-1/2
• 8 years agoHelpfull: Yes(26) No(0)
• If we calculate the average of the first two terms of the given sequence then we get,
  
  {1+(-2)}/2 = -0.5
  
  Similarly, average of the first 4 terms = (1-2+3-4)/4 = -0.5
  
  Similarly, average of the first 6 terms = -0.5
  
  Hence, for every even number of terms considered, the average will remain constant i.e., -0.5
  So average of first 200 terms will also be -0.5; since 200 is even.
• 8 years agoHelpfull: Yes(13) No(0)
• sum of 1st 2 terms = -1
  sum of 1st 4 terms = -2
  sum of 1st 6 terms = -3 and so on...
  hence sum of 1st 200 terms = -100
• 8 years agoHelpfull: Yes(4) No(0)
• n/2(a+l)
  100/2(1+199)=50*200=10000
  100/2(-2+-200)=50*-202=-10100
  so 10000-10100/200=-1/2
• 8 years agoHelpfull: Yes(2) No(1)
• since 1+(-2)= -1
  3+(-4) = -1
  .
  .
  .
  99+(-100)=-1 uptil 100 the sum=-50
  similarly for another 100 digits uptil 200 sum=-50
  total sum uptil 200 = -50 +(-50)= -100
  therefore, average= -100/200= -1/2
• 7 years agoHelpfull: Yes(2) No(0)
• Average=(1-2+3-4+5-6+7-8.......)/200
  = (-1-1-1-1......)/200
  =-100/200
  =-0.5
• 7 years agoHelpfull: Yes(1) No(1)
• a+(n-1)d=1+(200-1)(-1)=-98
• 8 years agoHelpfull: Yes(0) No(1)
• Series is divided into two terms 1,3,5.... will contain 100 terms
  and second series is -2 ,-4,-6
  S=n/2*(2a+(n-1)d)
  so first series give s=10000
  second series give s=-10100
  add the two series and divide it by 200
  so avg=-100/200
  ie ans=-0.5
• 8 years agoHelpfull: Yes(0) No(0)
• Average=(1-2+3-4+5-6+7-8...........)/200
  (-1-1-1-1-1-1-1......)/200
  -100/200=-0.5
• 7 years agoHelpfull: Yes(0) No(1)
• Answer will be -50
  
  Explanation
  -----------------
  we have
  1 ,-2, 3, -4, 5 ........
  rearrange and take sum,
  (1+3+5+7+....+199) - (2+4+6+8+....+200) ;both AP series has exactly 100 terms
  =100/2(1+199)-100/2(2+200)
  =50*200 - 50*202
  = -50*2
  average =-50*2/2
  = -50
• 7 years agoHelpfull: Yes(0) No(3)
• all even terms in the series are negative and all odd terms are positive ....200th term will be even...so the sum of 200 terms will be...(1+3+5+...+199) - (2+4+6+...+200)=-100
• 7 years agoHelpfull: Yes(0) No(0)
• for each two terms the difference will be -1 so for 200 terms it will be -100
  AVERAGE = - 100 / 200 = - 0.5
• 7 years agoHelpfull: Yes(0) No(0)
• avg of first two numbers is -1/2;
  avg of first three numbers is 2/3;
  then the avg of first 200 terms is -1/2
• 7 years agoHelpfull: Yes(0) No(0)
• L takes place after R
• 7 years agoHelpfull: Yes(0) No(1)
• -100
  1-2=-1
  3-4=-1.....100 times
• 7 years agoHelpfull: Yes(0) No(0)
• -0.5
  1-2=-1
  3-4=-1....100 times
  -100/200=-0.5
• 7 years agoHelpfull: Yes(0) No(0)
• 1-2+3-4+5=3 this is for first 5 numbers.let us consider it for all 200 terms as 200/5=40
  then 40*3=120
• 7 years agoHelpfull: Yes(0) No(1)
• (-100+101)/200=1/200
• 4 years agoHelpfull: Yes(0) No(1)