Fibonacci Sequence Calculator

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
• F₀ = Initial term of the given series
• F₁ = the second number of the series

Sum of the series = F_n = ∑_t=0ⁿ (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

F₀ = 0

F₁ = 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.

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.

F_n = ∑_t=0ⁿ (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 = F₈ = ∑_t=0⁸ (F_t)

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.

F_n = F_n-1 + F_n-2

Step 3:

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

F_n = ∑_t=0ⁿ (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 = F₁₂ = ∑_t=0¹² (F_t)

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