QuestionFind the next five terms of the Fibonacci sequence: $144, 233, 377, 610$ ?

Studdy Solution

STEP 1

Assumptions1. The given sequence is a Fibonacci sequence. The Fibonacci sequence is defined as each number is the sum of the two preceding ones, starting from0 and1.

STEP 2

The Fibonacci sequence is defined by the recurrence relation $(n) = F(n-1) + F(n-2)$ where $(n)$ is the nth term in the sequence.

STEP 3

We are given the first four terms of the sequence144,233,377,610. To find the next term, we add the last two terms.
$(5) = F() + F(3)$

STEP 4

Substitute the given values into the equation $() =610 +377$

STEP 5

Calculate the value of $(5)$ $(5) =610 +377 =987$

STEP 6

To find the sixth term, we add the fifth term and the fourth term $(6) = F(5) + F(4)$

STEP 7

Substitute the values into the equation $(6) =987 +610$

STEP 8

Calculate the value of $(6)$ $(6) =987 +610 =1597$

STEP 9

To find the seventh term, we add the sixth term and the fifth term $(7) = F(6) + F(5)$

STEP 10

Substitute the values into the equation $(7) =1597 +987$

STEP 11

Calculate the value of $(7)$ $(7) =1597 +987 =2584$

STEP 12

To find the eighth term, we add the seventh term and the sixth term $(8) = F(7) + F(6)$

STEP 13

Substitute the values into the equation $(8) =258 +1597$

STEP 14

Calculate the value of $(8)$ $(8) =2584 +1597 =418$

STEP 15

To find the ninth term, we add the eighth term and the seventh term $(9) = F(8) + F(7)$

STEP 16

Substitute the values into the equation $(9) =418 +2584$

STEP 17

Calculate the value of $(9)$ $(9) =418 +2584 =6765$ The next five terms of the Fibonacci sequence are987,1597,2584,418,6765.

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