Question
Fibonacci numbers Take $10$ numbers as shown below:
$a, b, (a + b), (a + 2b), (2a + 3b), (3a + 5b), (5a + 8b), (8a + 13b), (13a + 21b),$ and $(21a + 34b)$. Sum of all these numbers $= 11(5a + 8b) = 11 × 7th$ number.
Taking $a = 8, b = 13.,$
Write $10$ Fibonacci numbers and verify that sum of all these numbers $= 11 × 7th$ number
Hint. $I, II, (I + II), (III + II), (IV + III), [V + IV), $and so on

Answer

$a = 8$ and $b = 13$
The numbers are $8, 13, 21, 34, 55, 89, 144, 233, 377$ and $610.$
Sum of the numbers $= 8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 + 377 + 610 = 1584$
$11 \times 7th$ number $= 11 \times 144 = 1584$

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