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 + 34 b). Sum of all these numbers =11(5a + 8b) = 1 1 x 7th number.

Taking a = 8, b =13; write 10 Fibonacci numbers and verify that sum of all these numbers =11 x 7th number.

Answer 1

Here a = 8 and b = 13

The numbers in the Fibonacci sequence are arranged in the following manner:

1st, 2nd, (1st+2nd), (2nd+3th), (3th+4th), (4th+5th), (5th+6th), (6th+7th), (7th+8th), (8th+9th), (9th+10th)

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

11×7th number = 11×144=1584