Take a look at the series below: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ... To form the pattern, start by writing 1 and 1 . Add them together to get 2. Add the last two numbers: 1+2=3. Continue adding the previous two numbers to find the next number in the series. These numbers make up the famed Fibonacci sequence: previous two numbers are added to get the immediate new number.
Question
Take a look at the series below:
$1,1,2,3,5,8,13,21,34,55 \ldots$
To form the pattern, start by writing 1 and 1 . Add them together to get 2. Add the last two numbers: $1+2=3$.Continue adding the previous two numbers to find the next number in the series. These numbers make up the famed Fibonacci sequence: previous two numbers are added to get the immediate new number.
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Answer
The sequence provided is an example of the Fibonacci sequence where each number is the sum of the two preceding ones. Here's how the sequence is generated:
Start with the numbers 1 and 1.
To get the next number in the series, add the two previous numbers.
Here is the step-by-step formation of the sequence:
Start: (1, 1)
$1 + 1 = 2 \rightarrow 1, 1, 2$
$1 + 2 = 3 \rightarrow 1, 1, 2, 3$
$2 + 3 = 5 \rightarrow 1, 1, 2, 3, 5$
$3 + 5 = 8 \rightarrow 1, 1, 2, 3, 5, 8$
$5 + 8 = 13 \rightarrow 1, 1, 2, 3, 5, 8, 13$
$8 + 13 = 21 \rightarrow 1, 1, 2, 3, 5, 8, 13, 21$
$13 + 21 = 34 \rightarrow 1, 1, 2, 3, 5, 8, 13, 21, 34$
$21 + 34 = 55 \rightarrow 1, 1, 2, 3, 5, 8, 13, 21, 34, 55$
Important Points:
This pattern is known as the Fibonacci sequence.
Each number is the sum of the previous two numbers.
The sequence is often started with 0 and 1 in some variations, but the principle remains the same.
By continuing this process, you can generate as many Fibonacci numbers as needed.
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