High School Math : Understanding Sequences

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Summations And Sequences

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

\(\displaystyle \small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,...\)

Possible Answers:

\(\displaystyle 16,\ 21,\ 24\)

\(\displaystyle 21,\ 55,\ 63\)

\(\displaystyle 14,\ 17 ,\ 22\)

\(\displaystyle 18, \23,\ 28\)

\(\displaystyle 21,\ 34,\ 55\)

Correct answer:

\(\displaystyle 21,\ 34,\ 55\)

Explanation:

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

\(\displaystyle x_n=x_{n-1}+x_{n-2}\)

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

\(\displaystyle x_n=13+8=21\)

\(\displaystyle \small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21...\)

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

\(\displaystyle x_n=21+13=34\)

\(\displaystyle \small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21,\ 34...\)

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

\(\displaystyle x_n=34+21=55\)

\(\displaystyle \small 1,\1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21,\ 34,\ 55...\)

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