# 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.

Fn = Fn-1 + Fn-2

Here,

• Fn = nth Fibonacci number in the series
• Fn-1 = first previous number in the series
• Fn-2 = Second previous number in the series
• F0 = Initial term of the given series
• F1 = the second number of the series

Sum of the series = Fn = ∑t=0n (Ft)

## 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

F0 = 0

F1 = 1

Step 2:

Write the formula of the Fibonacci sequence.

Fn = Fn-1 + Fn-2

Step 3:

Put the values of “n” one by one up to the 8th term.

F0 = 0

F1 = 1

Put the value of “n=2”.

F2 = F1 + F0 = 1 + 0 = 1

Put the value of “n=3”.

F3 = F2 + F1 = 1 + 1 = 2

Put the value of “n=4”.

F4 = F3 + F2 = 2 + 1 = 3

Put the value of “n=5”.

F5 = F4 + F3 = 3 + 2 = 5

Put the value of “n=6”.

F6 = F5 + F4 = 5 + 3 = 8

Put the value of “n=7”.

F7 = F6 + F5 = 8 + 5 = 13

Put the value of “n=8”.

F8 = F7 + F6 = 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.

Fn = ∑t=0n (Ft)

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 = F8 = ∑t=08 (Ft)

F8 = {(F0) + (F1) + (F2) + (F3) + (F4) + (F5) + (F6) + (F7) + (F8)}

F8 = 0 + 1 + 1 + 2 + 3 + 5 + 8+ 13 + 21

Sum of the series = F8 = 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

F0 = 0

F1 = 1

Step 2:

Write the formula of the Fibonacci sequence.

Fn = Fn-1 + Fn-2

Step 3:

Put the values of “n” one by one up to the 12th term.

F0 = 0

F1 = 1

Put the value of “n=2”.

F2 = F1 + F0 = 1 + 0 = 1

Put the value of “n=3”.

F3 = F2 + F1 = 1 + 1 = 2

Put the value of “n=4”.

F4 = F3 + F2 = 2 + 1 = 3

Put the value of “n=5”.

F5 = F4 + F3 = 3 + 2 = 5

Put the value of “n=6”.

F6 = F5 + F4 = 5 + 3 = 8

Put the value of “n=7”.

F7 = F6 + F5 = 8 + 5 = 13

Put the value of “n=8”.

F8 = F7 + F6 = 13 + 8 = 21

Put the value of “n=9”.

F9 = F8 + F7 = 21 + 13 = 34

Put the value of “n=10”.

F10 = F9 + F8 = 34 + 21 = 55

Put the value of “n=11”.

F11 = F10 + F9 = 55 + 34 = 89

Put the value of “n=12”.

F12 = F11 + F10 = 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.

Fn = ∑t=0n (Ft)

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 = F12 = ∑t=012 (Ft)

F12 = {(F0) + (F1) + (F2) + (F3) + (F4) + (F5) + (F6) + (F7) + (F8) + (F9) + (F10) + (F11) + (F12)}

F12 = 0+1+1+2+3+5+8+13+21+34+55+89+144

Sum of the series = F12 = 376