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.

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Solution

Given:
$a = 8 a n d b = 13$
The numbers in the Fibonnaci sequence are arranged in the following manner:
$1 s t, 2 n d, (1 s t + 2 n d), (2 n d + 3 t h), (3 t h + 4 t h), (4 t h + 5 t h), (5 t h + 6 t h), (6 t h + 7 t h), (7 t h + 8 t h), (8 t h + 9 t h), (9 t h + 10 t h)$

The numbers are $8, 13, 21, 34, 55, 89, 144, 233, 377 and 610$ .
Sum of the numbers = $8 + 13 + 21 + 34 + 55 + 89 + 144 + 233 + 377 + 610$
$= 1584$
$11 \times 7 t h n u m b e r = 11 \times 144 = 1584$

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