Question

The​ 18th, 19th and 20th numbers in the Fibonacci sequence​ are, respectively,​ 2584, 4181, and 6765. What is the 21st​ number?

Answer 1

Answer:

4181  +  6765  =  10946

Step-by-step explanation:

Fibonacci Sequence: The $\textbf{n}^{\textbf{th}}$ term of a Fibonacci Sequence is given by the sum of the immediate two previous numbers.

In mathematical notation:  $\textbf{x}_{\textbf{n}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{x}_{\textbf{n - 1}} \hspace{1mm} \tetxbf{+} \hspace{1mm} \textbf{x}_{\textbf{n - 2}}$

Hence, $21^{st}$ number = $20^{th}$ number + $19^{th}$ number.

= 4181   +    6765

= 10946 which is the required answer.