For a Fibonacci sequence, from the third term onwards, each term in the sequence

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 in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence?

  1. 76
  2. 108
  3. 123
  4. 147

Answer

Let 6th and 7th term of Fibonacci series be x and y respectively.

y2 - x2 = 517

(y - x) * (y + x) = 517

Prime factorization of 517 = 11*47

y - x = 11 and y + x = 47

y = 29 and x = 18

6th Term = 18 and 7th Term = 29

8th term = 18 + 29 = 47

9th Term = 29 + 47 = 76

10th term = 47 + 76 = 123

The correct option is C.