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

• here if we add two consecutive numbers then we get -1
  and then the average would like -1/2
  so for 200 terms average will be -100/200
  which is -0.5
• 9 years agoHelpfull: Yes(35) No(0)
• 1-2=-1
  3-4=-1
  5-6=-1
  ...........for 6 numbers we get 3*-1
  like that for 200 nos we get 100*-1
  then -0.5
• 9 years agoHelpfull: Yes(5) No(0)
• find out even or odd no. by this eqen. : = n/2(a+l)
  = 1,3,5,7..... = total n=100
  = -2,-4,...... = total n=100
  So, 100/2(1+199) = 10,000
  and 100/2(-2+(-200)) = -10,100
  = (10,100 - 10,000)/200
  = -0.5
• 9 years agoHelpfull: Yes(4) No(1)
• -0.5
  consider the first two numbers, their sum is -1. there will be 100 such pairs as 200 terms are considered.
  so total sum will be -100. average=-100/200=-0.5
• 9 years agoHelpfull: Yes(3) No(1)
• 1-2=-1
  2-3=-1
  .
  .
  ..
  so there are 100 such pairs whose sum is -1
  
  Therfore, (-1*100)/200
  =-100/200
  = -1
• 9 years agoHelpfull: Yes(1) No(8)
• 1+(-2)=-1
  3+(-4)=-1
  5+(-6)=-1
  total no of such pairs will be 100
  and each pair will give -1 result
  so adding -1,100 times will result in -100.
  so answer is= -100
• 9 years agoHelpfull: Yes(1) No(4)
• we have one formula for find sum of 1+3+5+.................
  S=(n/2)[2a+(n-1)d]
  here
  n is how many terms are there in series
  a is first term of this series
  d is diff between two numbers
  
  first we find out 1+3+5+7 series
  S=(100/2)[2*1+(100-1)2]
  50*(2+198)
  =10000
  then 2+4+6+8+.........
  s=(100/2)[2*2+99*2]
  50*202
  =10100
  That is in negetive series -10100
  next 10000-10100
  we get -100
  then average is -100/200
  we get -0.5
  ans is -0.5
  
  
  
  
  
• 9 years agoHelpfull: Yes(1) No(0)
• (1+3+5+............+(2*100-1))-(2+4+6+...............+2*100)=100*100-(100*100+100)=-100;
  so avg.=-100/200(total terms)=-.5
• 9 years agoHelpfull: Yes(0) No(1)
• n(n+1)/2
  20100
• 9 years agoHelpfull: Yes(0) No(3)
• ans:0.5
  (1-2+3-3+5-6....200)/200=100/200=0.5
• 9 years agoHelpfull: Yes(0) No(3)
• Start pairing of 2numbs then we will get 100 pairs avg of each pair will be -0.5 fr ex avg of 1&-2 is -05
  Then fr 100 pairs =(100*(-.5))/100 = -0.5
• 9 years agoHelpfull: Yes(0) No(1)
• ans:0.5
  (1-2+3-3+5-6....200)/200=-100/200=-0.5
• 9 years agoHelpfull: Yes(0) No(1)
• answer is -0.5
• 9 years agoHelpfull: Yes(0) No(2)
• {(1+3+5...........199)-(2+4+6......200)}/200= -1
• 9 years agoHelpfull: Yes(0) No(2)
• { (1+3+5+7....199) - (2+4+6+....200) } / 200 = 100/2(2*1+(100-1)2) - 100/2(2*2+(100-1)2)
  = 1/2
• 9 years agoHelpfull: Yes(0) No(1)
• Ans: 0.5
  -
• 9 years agoHelpfull: Yes(0) No(1)
• sum of odd numbers=n^2 i.e 1 to 199 -> 100 numbers=(100)^2
  sum of even numbers=n(n+1) i.e 2 to 200 -> 100 numbers=100*101
  
  
  (10000-10100)/200=-0.5
  
• 9 years agoHelpfull: Yes(0) No(1)