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

a]19284756374
b]243768954321
c]287621088425
d]357849113670

• 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
• 9 years agoHelpfull: Yes(10) No(1)
• 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
• 9 years agoHelpfull: Yes(3) No(0)
• Observing the sequence 1, 6, 7, 13, 20, 33, and so on,
  It can be re-written as 1, (1+5), (2+5), (3+10), (5+15), (8+25), and so on.
  
  The sequence thus decomposes into sum of two standard Fibonacci sequences,
  1, 1, 2, 3, 5, 8, 13 up to 40 terms and 5*(1, 1, 2, 3, 5, 8, 13 up to 39 terms.
  
  So the sum is given as : Sum of 40 terms of the standard Fibonacci series + 5*Sum of 39 terms of the standard Fibonacci series. Which is equivalent to 6*Sum of 39 terms in the standard Fibonacci series + the 40th term. And since sum of n terms of a fibonacci series is given as F(n+2)-1,
  
  The sum should be 6*{F(41)-1}+F(40) = F(40) + 6*F(41) - 6.
  
• 9 years agoHelpfull: Yes(2) No(1)
• Option A as it is even & non zero.
• 9 years agoHelpfull: Yes(0) No(9)
• 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
• 9 years agoHelpfull: Yes(0) No(0)