Understanding Sequences - High School Math

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Question

Consider the Fibonacci sequence written below. What are the next three terms?

$\small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,...$

Answer

Each number in the Fibonacci sequence can be calculated by the sum of the previous two numbers.

$x_n=x_{n-1}+x_{n-2}$

The next term in the sequence will be the sum of the two terms preceding it: 8 and 13.

$\small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21...$

The next term will be the sum of 13 and 21.

$\small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21,\ 34...$

The next term will be the sum of 21 and 34.

$\small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21,\ 34,\ 55...$

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