Question

Use F40 = 63; 245; 986 and F38 = 39; 088; 169 to find the value of F39. Show your reasoning. (3) Using the Binet’s formula, calculate F4.

Answer 1

Answer:

By, using Binet’s formula we have $F_{39} =$ 24; 157; 817.

Concept:

The generalized Fibonacci p-numbers, sums, combinatorial representations, and generating function of the generalized Fibonacci p-numbers are provided after the generalized Binet formula. Additionally, we develop an explicit formula for the sums of the generalized Fibonacci p-numbers using matrix methods. We take into consideration a generalization of the famous Fibonacci numbers, often known as Fibonacci -numbers.

Given:

$F_{40}$ = 63; 245; 986

$F_{38}$ = 39; 088; 169

Find:

By using Binet's formula find $F_{39}$.

Solution:

We have to find Fibonacci numbers of $F_{39}$.

$F_{(n + 1)} = F_{n} + F_{(n - 1)} \\F_{40} = F_{39} + F_{38} \\F_{39} = F_{40} - F_{38}$

$F_{39} =$ 63; 245; 986 - 39; 088; 169

$F_{39} =$ 24; 157; 817

Hence, the value of $F_{39} =$ 24; 157; 817.

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