N the set of natural numbers is partitioned into subsets S1 = (1), S2 = (2,3), S3 ={4,5,6), S4 = {7,8,9,10} and so on.The sum of the elements of the subset S50 is??CAT 1990

1) 61250
2) 65525
3) 42455
4) 62525

• s1=(1) s2(2,3), s3(4,5)................
  
  we have to find sum of set s50( ) ??
  
  Look each set carefully numbers seems to be like 1,2,3,4,5,6,7,8,9,10,..............
  
  hence s50 set contain 50 element
  
  and s49 contain 49 element
  
  then sum of 1st 49 terms 1+2+3+4+5+6+7+8+9+10,..............48+49
  
  n(n+1)/2 =49(49+1)/2=1225
  
  that means last element of s49 is 1225.
  
  
  hence first element of s50 is start from 1226
  
  and last element is 1225+50=1275.
  
  so the element in the s50(1226,1227,1228.............1275)
  
  so sum= n/2(2a+(n-1)d) by airthemetic mean formula
  
  put the value
  
  => 50/2(2*1226+(50-1)1)
  
  =>625625
  
  option 4 is right answer
  
• 8 years agoHelpfull: Yes(1) No(0)
• There's a nice formula that says: The sum 1+2+3+...+n = (n)(n+1)/2
  So, 1+2+3+4+27+28+.......48+49 = (49)(50)/2, which equals 1225
  This means there are 435 numbers in the subsets from S1 to S50.
  In other words, S49 = {1177,1178.1179..............1225}
  
  So, S50 = {1226,1227.1228,..............1275}
  We're asked to find the sum of 1226+1227+1228+,..............+1275
  
  There several different options here, but the fastest is to use the answer choices to our advantage.
  
  Notice that if all 30 numbers in S50 were 1226 (the smallest number in the set), then the sum would be (50)(1226) = 61300
  This means that the sum of 1226+1227+1228+,..............+1275 must be greater than 61250 (eliminate answer choice (1),(3)
  
  Now notice that if all 50 numbers in S50 were 1275 (the biggest number in the set), then the sum would be (50)(1275) = 63750
  This means that the sum of 1226+1227+1228+,..............+1275 must be less than 63750(eliminate answer choices (2)
  
  This leaves us with 4, the correct answer.
  
• 8 years agoHelpfull: Yes(0) No(1)