1,2,2,3,3,3,4,4,4,4,1,1,2,2,2,2,3,3,3,3,3,3,4....... what is the 2888th number in this sequence???

• let consider 1st sequence 1-1,2-2,3-3,4-4= total 10 terms
  let consider 2nd sequence 1-2,2-4,3-6,4-8= total 20 terms
  let consider 3rd sequence 1-3,2-6,3-9,4-12= total 30 terms
  let consider 4th sequence 1-4,2-8,3-12,4-16= total 40 terms and so on...
  so the series is in A.P
  10,20,30,40,50,60,......
  10(1+2+3+4+5+6+....n)=x where x is the near value to the given 2888th number
  w.k.t sum of n terms =n(n+1)/2
  10{n(n+1)/2}=x(nearer to 2888)
  by trail and error method we get n=23
  and we get x=2760
  no.of more terms=2888-2760=128
  as 23 is completed we have start with 24 digit i.e
  24-1,48-2,72-3,96-4
  as we add no.of 1's and 2's we get 72
  as we add no.of 1's and 2's and 3's we get 144
  so the required number "128" is in between 72(1's+2's) and 144((1's+2's+3's)
  so the 128th number is "3".finally the 2888th number is "3"
• 11 years agoHelpfull: Yes(59) No(13)
• 1,22,333,4444 : 10 terms
  11,2222,333333,44444444 : 20 terms
  1111,22222222,333333333333,4444444444444444 : 40 terms
  next 1's-8, 2's-16, 3's-24, 4's-32 total: 80 terms and so on...
  10+20+40+80+160+320+640+1280=2550
  next sequence will be 256 1's and 512 2's
  2550+256=2806
  2806+512 crosses the limit...
  therefore the 2888th term will be 2
• 11 years agoHelpfull: Yes(55) No(1)
• 2 will be the term
• 11 years agoHelpfull: Yes(14) No(7)
• 3 is the answer
• 11 years agoHelpfull: Yes(10) No(6)
• Can you explain how you got the answer ?
• 11 years agoHelpfull: Yes(4) No(1)
• 1 should be the ans..
  
• 11 years agoHelpfull: Yes(3) No(5)
• 1 is the ans
• 11 years agoHelpfull: Yes(2) No(5)
• what is explanation of this question??
  
• 11 years agoHelpfull: Yes(2) No(1)
• what is the explanation of the answer
• 11 years agoHelpfull: Yes(1) No(1)
• chaitanya pls explain the answer
  
• 11 years agoHelpfull: Yes(1) No(1)
• @krishna
  the number of terms doubles at each iteration..
  so it is 10,20,40,80,terms and not 10,20,30,40..
• 11 years agoHelpfull: Yes(1) No(1)
• 4,4,4,4,4,4,4 be
• 11 years agoHelpfull: Yes(0) No(3)
• In the series there are 10 terms in the series 1,2,2,3,3,3,4,4,4,4.
  Next will be 20 terms, followed by 40 terms, 80 terms and so on.
  10+20+40+80+160+320+640 = 1270th term will end with 4.
  Out of next 640*2 = 1280 terms, first 128 will be 1s, next 256 terms will be 2s, next 384 terms will be 3s and the next 512 terms will be 4s.
  2320 - 1270 = 1050 which is 128+256+384+282. Hence the number will be 4.
  
• 11 years agoHelpfull: Yes(0) No(1)
• the 2888th number is "3"
• 11 years agoHelpfull: Yes(0) No(1)
• please suggest anyone what happen if 1,2,2,3,3,3,4,4,4,4,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4.......what is the 2898th number in the sequence....its challenge and please explain he procedure too..
  
• 9 years agoHelpfull: Yes(0) No(0)