Video: Number Patterns with Integer Numbers

Write the next two terms in the following sequence: 3, 5, 8, 13, 21, _, _.


Video Transcript

Write the next two terms in the following sequence: three, five, eight, 13, 21.

In order to work out the next few terms in a sequence, we usually look for a term-to-term pattern. In this sequence, to get from three to five, we add two. We add three to get from five to eight. We add five to get from eight to 13. And we add eight to get from 13 to 21. In this question, however, there is no obvious link between these numbers. This is because this sequence is a special one known as the Fibonacci sequence.

In order to find the next number in the Fibonacci sequence, we need to add the two numbers before it. We can see already that three plus five is equal to eight. Five plus eight is equal to 13. And eight plus 13 is equal to 21. In order to find the first missing number, we need to add 13 and 21. This is equal to 34. The second missing number can be calculated by adding 21 and 34. This is equal to 55. The next two numbers in the sequence three, five, eight, 13, 21 are 34 and 55.

The mathematician known as Fibonacci lived between 1170 and 1250 in Italy. And Fibonacci Day is celebrated on November the 23rd each year. The Fibonacci sequence has many practical applications, including the spiral found in nature and the golden ratio. If you have time, it would be worth looking these up and exploring them further.

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