For a Fibonacci sequence, from the third term onwards, each
term in the sequence is the sum of the previous two terms in that sequence.
If the difference of squares of seventh and sixth terms of this sequence is
517, what is the tenth term of this sequence?
(a) 147 (b) 76
(c) 123 (d) Cannot be determined

• (a7)^2 - (a6)^2 = 517
  (a7 + a6)(a7 - a6) = 47*11
  
  a7 +a6 = 47
  a7 - a6 = 11 = a5
  
  a5=11
  a6 = 18
  a7 = 29
  a8 = 47
  a9 = 76
  so
  a10= 123
• 12 years agoHelpfull: Yes(9) No(0)
• If we consider
  (a7)^2 - (a6)^2 = 517
  (a7 + a6)(a7 - a6) = 47*11 = 517*1 = (-47)*(-11) = (-1)*(-517)
  
  then answer will be different.
  
  If negative numbers in series are allowed ( which are not allowed in normal finonacci sequence),
  
  tenth term can not be unique.
  Then can not be determined.
  
  
• 12 years agoHelpfull: Yes(3) No(0)
• Fibonacci sequence can have negative numbers as per link below...
  
  http://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers
• 12 years agoHelpfull: Yes(1) No(0)