Question

For a Fibonacci sequence, from the third term onwards, each term is the sum of the previous two. If the difference in squares of the 7th and 6th terms is 517, what is the 10th term?

• A. 147
• B. 76
• C. 123
• D. Cannot be determined

Hint:

Use Fibonacci identities: $F_{n+1}^2 - F_n^2 = F_{n-1}F_{n+2}$.

Answer 1

The Correct Option is A

Let $F_6, F_7$ be terms. $F_7^2 - F_6^2 = (F_7 - F_6)(F_7+F_6) = F_5(F_8) = 517$. Since $F_8 = F_6 + 2F_5$, solve small Fibonacci integer pairs to match 517. Sequence found: $F_5=11, F_6=18, F_7=29$, then $F_{10}=147$.