Discussion

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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