a series is given as 1,6,7,13,20,33....and so on.find the sum of first 52 terms?

• Ans: 352849113670
  1st and 2nd terms are 1,6
  3rd term is 7 which is sum of first+second.
  4th term is 13 which is sum of second + third.
  Expanding the series further by adding a few more terms, it is 
  1, 6, 7, 13, 20, 33, 53, 86, 139 and so on.
  
  Now if we add the terms for upto 1,2,3,4,5,6 terms it is 
  1, 7, 14, 27, 47, 80, 133, 219 and so on.
  
  Hence we can infer the sum upto Nth term is (N+2)nd term - 6
  As 1+6+7 is sum upto 3 terms and it is 5th term minus 6= 20-6 = 14
  As 1+6+7+13+20+33+53 is sum upto 7 terms and it is 9th term minus 6 = 139-6 = 133
  
  Hence sum upto 52nd term is nothing but 54th term -6.
  
  Now our task is to find 54th term.
  Using the golden ratio we can easily find the 54th term. But we will just find few more terms for accuracy.
  1, 6, 7, 13, 20, 33, 53, 86, 139, 225, 364, 589, 953, 1542 which is upto 14 terms.
  
  So 54th term = 1542 * (1.6180339)^40 = 352849113676 approx
  Hence sum will be 352849113676-6 = 352849113670
  
• 11 years agoHelpfull: Yes(20) No(5)
• For fibonacii number :-
  the formula of sum of fibonacci series is S(n)=F(n+2)-F(2)
  So first we have to find the 54th term.. we will get the sum of 52 termu
  I have checked the formula for 10,12,13. But anyone suggest technique for faster calulation of nth term of fibonacci series..
• 11 years agoHelpfull: Yes(10) No(3)
• ans:53
  adjacent 2no's can be added.which gives the third number.....this cycle can be repeated..
• 11 years agoHelpfull: Yes(6) No(61)
• sry...i can't read the full question
• 11 years agoHelpfull: Yes(3) No(1)
• ans:53
  adjacent 2no's can be added.which gives the third number.....this cycle can be repeated.
  
  
• 10 years agoHelpfull: Yes(3) No(1)
• can anyone suggest the shortcut to identify nth fibonacci term..?
• 11 years agoHelpfull: Yes(2) No(2)
• u r grt sireesha
• 11 years agoHelpfull: Yes(0) No(13)
• (2*52-3)*(2*52-2)/2=101*102/2=101*51=5151
  i m nt sure sneha...
• 11 years agoHelpfull: Yes(0) No(7)
• it suggests we need to find out the 54th term of the sequence if we need to find the sum upto 52nd...
  according to the binets formulae the answer would be=8626757126
• 11 years agoHelpfull: Yes(0) No(0)
• 53 is the ans.
• 11 years agoHelpfull: Yes(0) No(2)
• 1,6,7,13,20 ...Find sum up to 52 terms
  
  Solution:
  Nth term =a+ (n-1) d
  =1+ (52-1)5
  =256
• 8 years agoHelpfull: Yes(0) No(0)