1 2 1 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 2 1 .........,sum of first 1230 terms of series.

• 
  We have to find the no. of 1's and no. of 2's in 1230 terms...
  Lets take 1st two terms ... 1, 2
  no. of 1's is 1 nd no. of 2's is 1 => (1+1)
  1st 5 terms ... 1,2,1,2,2
  => (1+1)+(1+2)
  1st 9 terms ... 1,2,1,2,2,1,2,2,2
  => (1+1)+(1+2)+(1+3)
  => (1+1+1)+(1+2+3)
  3 + 3(3+1)/2
  [Its of the form n + n(n+1)/2].
  So in 1st n terms, no. of 1's is "n", no. of 2's is n(n+1)/2
  So sum of 1st n terms ll be n*1 + n(n+1)
  So for the 1230 terms,
  n + n(n+1)/2
  n=48
  48 + 48*49/2 = 1224 and next 6 no. are 1+2+2+2+2+2 = 11
  So total sum will be = 48*1 + 48*49 + 11 = 2411
  Ans : 2411
• 9 years agoHelpfull: Yes(19) No(0)
• Group the no. As follows:
  
  X= {1, 2+1, 2+2+1, 2+2+2+1, 2+2+2+2+1,…}
  
  Now it gives you A.P. as follows:
  
  Y= {1, 3, 5, 7, 9,…}
  
  Number of terms contained in each Y is:
  
  Z= {1, 2, 3, 4, 5…}
  
  Given the sum to be found ulti 1230 terms but 1230 doesn't give you the exact number if you solve it by sum of n natural no.s formulae. So break 1230 into 1225+5.
  
  Now find the value of n given the sum is 1225.
  
  n(n+1)/2 = 1225
  
  This gives n=49
  
  Now use the sum of A.P. formulae in Y:
  
  Sum= n[2a+(n-1)d]/2
  
  Where n=49, a=1, d=2 we get:
  
  Sum = 2401
  
  Now this is the result for 1225 no.s
  
  To get the result of 1230 no.s we need to add the next 5 numbers in the sequence (which starts with 2). So the next 5 terms are 2,2,2,2,2.
  
  Therefore =2*5 = 10
  
  Final result is 2401+10 = 2411
• 8 years agoHelpfull: Yes(11) No(0)
• Start with making two series
  1+1*2=3 terms 2
  1+2*2=5. 3
  1+3*2=7. 4
  ....
  ....
  ....
  1+47*2=95. 48
  1+48*2=97. 49
  
  And last term
  1+5*2=11. 6
  Total sum= 48(3+97)/2+11=2411
• 9 years agoHelpfull: Yes(4) No(0)
• 1 occuring at positions 1,3,6,10 & ......so on.it is of the format n*(n+1)/2. So now n*(n+1)/2=1230. Or n*(n+1)=2460. So putting n=49 in the equation we get no of occurrnce of 1. So remaing are digit 2.and the no. 2's are 1230-49=1189.this 1189 are the no. Of 2. So their sum will be 1189*2=2362.so total=sum of 2 + sum of 1= 2362+49=2411.
• 9 years agoHelpfull: Yes(3) No(2)
• 2313 is the answer
  
• 9 years agoHelpfull: Yes(0) No(2)
• 2411 is correct ans
• 9 years agoHelpfull: Yes(0) No(0)
• Which book u r referring to solve this type of questions
• 7 years agoHelpfull: Yes(0) No(0)