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 seventh and sixth terms of this sequence is 517, what is the tenth term of this sequence?
Explanation:
Let the nth term of the series be Fn.
∵ (F7)2 – (F6)2 = 517
∴ (F7 + F6)(F7 – F6) = 517
∴ (F7 + F6) (F7 – F6) = 11 × 47
∴ F8 × (F6 + F5 – F6) = 11 × 47
∴ F8 × F5 = 11 × 47
∴ F8 = 47 and F5 = 11
∴F8 = F7 + F6 = 2F6 + F5 = 3F5 + 2F4
∴ F4 = 7
Now the series F4 onwards is: 7, 11, 18, 29, 47, 76, 123
∴ The 10th term will be 123.
Hence, option (c).
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