Question

The sum of the first ten Fibonacci numbers is equal to the .......... times the seventh number.​

Answer 1

Answer:

the tenth Fibonacci number is Fib(10) = 55. The sum of its digits is 5+5 or 10 and that is also the index number of 55 (10-th in the list of Fibonacci numbers). So the index number of Fib(10) is equal to its digit sum. This time the digit sum is 8+9 = 17.

www.maths.surrey.ac.uk › fibmaths

The Mathematical Magic of the Fibonacci Numbers

Answer 2

From the given question the correct answer is:

11

The sum of the first ten Fibonacci numbers is equal to the 11 times the seventh number.​

Let the sequence of any 10 consecutive Fibonacci numbers is given by  

a,b,a+b,a+2b,2a+3b,3a+5b,5a+8bF7,8a+13b,13a+21b,21a+34b

(a)+(b)+(a+b)+(a+2b)+(2a+3b)+(3a+5b)+(5a+8b)F7+(8a+13b)

+(13a+21b)+(21a+34b)

=55a+88b=11(5a+8b)F7=11×7th term