If two consecutive terms are removed from a series 1,2...........n ,then the average of remaining terms is 261/4.what is the no of terms?

• Solve this problem from option.
  So from option 50 is the solution.
  So sum of first 50 numbers is (50*51)/2=1275
  Again after remove of 2 number, the avg of 48 number is 26 1/4=105/4
  so sum of 48 number is 48*(105/4)=1260
  so sum of two consecutive no is 15 which are 7 and 8.
• 9 years agoHelpfull: Yes(16) No(1)
• can anyone please explain it better
• 9 years agoHelpfull: Yes(3) No(1)
• n(n+1)/2-{K-(k-1)}=(n-2)*105/4
  so from here we can say that
  (n-2) is divisble by 4 as the total sum is a integer
  from here we can choose the answer from multiple choice
  
• 9 years agoHelpfull: Yes(2) No(2)
• for consecutive terms use formula
  last digit+first digit /2
  so,
  n+1/2 = 105/4
  n=52
  so,
  52-2
  =50
• 9 years agoHelpfull: Yes(2) No(2)
• Suppose we remove the number k and k+1. Then sum of remaining numbers is:
  [Math Processing Error]
  Dividing this by n-2 will give us the arithmetic mean.
  [Math Processing Error] ... (1)
  
  Notice that [Math Processing Error] is in its simplest form. So, we can conclude that the numerator of (1) is 261x and the denominator is 4x for some integer x.
  [Math Processing Error]
  So, n=4x+2 for some integer x
  Substituting in the equation and simplifying, we get:
  [Math Processing Error]
  So we must find positive integers x and k which satisfy this equation. Also, 4x+2>k as k and k+1 must be in 1..n
  Solve this to get the answer.
  One solution is n=130 and k=81
• 9 years agoHelpfull: Yes(1) No(10)
• average of n terms = n(n+1)/2*n = n+1/2 hence it should be in the form of integer or some Integer.5
  when 2 consecutive terms are removed max change in avg can be -1 to +1 final avg is 65.25
  hence actual avg may be 64.5 or 65 / 65.5 / 66
  hence n+1 = 129 or 130 or 131 or 132
  n= 128 / 129/130/131
  but n-2 should be a multiple of 4 as when 2 no.s are removed denominator has 4.
  only 130-2 =128 is divisible by 4
  hence n= 130
• 9 years agoHelpfull: Yes(0) No(3)