Question

If a and b are nth and n+1th Fibonacci numbers respectively then (n+5)th Fibonacci number is

1. 3a + 5b
2. a+b
3. 5a + 5b
4. a+b+5​

Answer 1

Answer:

1. 3a + 5b

Step-by-step explanation:

Fibonacci numbers have a property that, any term in the series is equal to sum of 2 previous terms.

Example of a Fibonacci series is

1, 1, 2, 3, 5, 8, 13, 21, 34, .......

Given that nth term = a

n+1 term = b.

n+2 term = n+1 term + n term. = b + a

n+3 term = n+2 term + n+1 term = (b+a) + b = 2b + a

n+4 term = (2b+a) + b + a = 3b + 2a

n+5 term = (3b + 2a) + (2b + a) = 5b + 3a.

Hence answer is 1st choice.