The sum of first 40 terms 1,6, 7,12, 13,20 …. ?

• [1, 7, 13.......20 terms] + [6, 12, 20......20 terms]
  [1 + (20-1)*6 ] + [this forms (n+1) (n+2)]
  117 + [ n^2 + 3n + 2]
  117 + 2870 + 630 + 2
  = 3715
• 10 years agoHelpfull: Yes(6) No(7)
• 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.
  
  Check the values!
• 10 years agoHelpfull: Yes(2) No(5)
• 1 add & 1 delete on series
  ans 2420
• 10 years agoHelpfull: Yes(1) No(1)
• hw can we find F(41),F(40) shekhar sir.
• 10 years agoHelpfull: Yes(1) No(0)
• you missed the 12 in the series..
  
• 10 years agoHelpfull: Yes(0) No(0)
• by using the formulas an=a1+(n-1)d and
  sn=n(a1+an)/2 we can get the solution
  
• 10 years agoHelpfull: Yes(0) No(2)
• please explain solution for this more clearly....
• 10 years agoHelpfull: Yes(0) 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.
  
  Check the values!
• 10 years agoHelpfull: Yes(0) No(1)
• ans 5443
  divide into two parts
  20 terms of 1,7,13 an a.p use formula
  an for other on 6=3*2
  12=3*4
  and so one then calculate values and add....seens lenghti but takes only 2 mins
• 10 years agoHelpfull: Yes(0) No(0)