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# Fibonacci Sequence Calculator

To use Fibonacci Sequence calculator, enter the nth term, and hit the calculate button

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## Fibonacci Sequence Calculator

Fibonacci Sequence Calculator is used to calculate the Fibonacci sequence up to any selected number. Moreover, it finds the sum of the all series of the term.

## What is Fibonacci Sequence?

Every number belongs to the number series of the Fibonacci sequence which is the addition of the last two terms. This sequence starts with 0 and 1 and added subsequently the two previous numbers generated the next number.

To make the new Fibonacci number keep in mind the below points.

- It always starts from 0 & 1.
- To find the next number in the sequence, add the two preceding numbers.

For Example,

0+1=1

1+1 =2

1 + 2 = 3

2 + 3 = 5

Hence, (0, 1, 1, 2, 3, 5) is the result.

## Formula

The mathematical formula of the Fibonacci sequence is stated below.

**F _{n} = F_{n-1} + F_{n-2}**

Here,

- F
_{n}= n^{th}Fibonacci number in the series - F
_{n-1 }= first previous number in the series - F
_{n-2}= Second previous number in the series - F
_{0}= Initial term of the given series - F
_{1}= the second number of the series

**Sum of the series = F _{n} = ∑_{t=0}^{n} (F_{t})**

## How to calculate the Fibonacci Sequence?

**Example 1:**

Find the Fibonacci number up to the 8 terms.

**Solution**

**Step 1:**

**The very first two values of the Fibonacci sequence are**

F_{0} = 0

F_{1} = 1

**Step 2:**

**Write the formula of the Fibonacci sequence.**

F_{n} = F_{n-1} + F_{n-2}

**Step 3:**

**Put the values of “n” one by one up to the 8 ^{th} term.**

F_{0} = 0

F_{1} = 1

**Put the value of “n=2”.**

F_{2} = F_{1} + F_{0} = 1 + 0 = 1

**Put the value of “n=3”.**

F_{3} = F_{2} + F_{1} = 1 + 1 = 2

**Put the value of “n=4”.**

F_{4} = F_{3} + F_{2} = 2 + 1 = 3

**Put the value of “n=5”.**

F_{5} = F_{4} + F_{3} = 3 + 2 = 5

**Put the value of “n=6”.**

F_{6} = F_{5} + F_{4} = 5 + 3 = 8

**Put the value of “n=7”.**

F_{7} = F_{6} + F_{5} = 8 + 5 = 13

**Put the value of “n=8”.**

F_{8} = F_{7} + F_{6} = 13 + 8 = 21

**Fibonacci series = {0, 1, 1, 2, 3, 5, 8, 13, 21}**

**Step 4:**

**To find the sum of the numbers use the below formula.**

F_{n} = ∑_{t=0}^{n} (F_{t})

**Step 5:**

**Put “n=8” to find the sum of the series up to 8 and put the value carefully to simplify.**

Sum of the series = F_{8} = ∑_{t=0}^{8} (F_{t})

F_{8} = {(F_{0}) + (F_{1}) + (F_{2}) + (F_{3}) + (F_{4}) + (F_{5}) + (F_{6}) + (F_{7}) + (F_{8})}

F_{8} = 0 + 1 + 1 + 2 + 3 + 5 + 8+ 13 + 21

**Sum of the series = F _{8} = 54**

**Example 2:**

Find the Fibonacci number up to the 12 terms.

**Solution**

**Step 1:**

**The very first two values of the Fibonacci sequence are**

F_{0} = 0

F_{1} = 1

**Step 2:**

**Write the formula of the Fibonacci sequence.**

F_{n} = F_{n-1} + F_{n-2}

**Step 3:**

**Put the values of “n” one by one up to the 12 ^{th} term.**

F_{0} = 0

F_{1} = 1

**Put the value of “n=2”.**

F_{2} = F_{1} + F_{0} = 1 + 0 = 1

**Put the value of “n=3”.**

F_{3} = F_{2} + F_{1} = 1 + 1 = 2

**Put the value of “n=4”.**

F_{4} = F_{3} + F_{2} = 2 + 1 = 3

**Put the value of “n=5”.**

F_{5} = F_{4} + F_{3} = 3 + 2 = 5

**Put the value of “n=6”.**

F_{6} = F_{5} + F_{4} = 5 + 3 = 8

**Put the value of “n=7”.**

F_{7} = F_{6} + F_{5} = 8 + 5 = 13

**Put the value of “n=8”.**

F_{8} = F_{7} + F_{6} = 13 + 8 = 21

**Put the value of “n=9”.**

F_{9} = F_{8} + F_{7} = 21 + 13 = 34

**Put the value of “n=10”.**

F_{10} = F_{9} + F_{8} = 34 + 21 = 55

**Put the value of “n=11”.**

F_{11} = F_{10} + F_{9} = 55 + 34 = 89

**Put the value of “n=12”.**

F_{12} = F_{11} + F_{10} = 89 + 55 = 144

**Fibonacci series = {0,1,1,2,3,5,8,13,21,34,55,89,144}**

**Step 4:**

**To find the sum of the numbers use the below formula.**

F_{n} = ∑_{t=0}^{n} (F_{t})

**Step 5:**

**Put “n=12” to find the sum of the series up to 12 and put the value carefully to simplify.**

Sum of the series = F_{12} = ∑_{t=0}^{12} (F_{t})

F_{12} = {(F_{0}) + (F_{1}) + (F_{2}) + (F_{3}) + (F_{4}) + (F_{5}) + (F_{6}) + (F_{7}) + (F_{8}) + (F_{9}) + (F_{10}) + (F_{11}) + (F_{12})}

F_{12} = 0+1+1+2+3+5+8+13+21+34+55+89+144

**Sum of the series = F _{12} = 376**