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Consider a sequence defined similarly to the Fibonacci, but with a slight twist:

f(n) = f(n-1)-f(n-2) with f(1) = 2 and f (2) = 5

Generate terms f (3), f(4), f(5), f(6), f(7), and f(8). Then, determine the value of f(25). ​

Sagot :

753-7527-8589 determine
MrRoyalidn

A sequence can be arithmetic, geometric, and it can take several other forms such as Fibonacci.

  • The values of f(3), f(4), f(5), f(6), f(7), and f(8) are 3, -2, -5, -3, 2, 5
  • The value of f(25) is 2

The given parameters are;

[tex]\mathbf{f(n) = f(n-1)-f(n-2)}[/tex]

[tex]\mathbf{f(1) = 2 }[/tex]

[tex]\mathbf{f(2) = 5 }[/tex]

Calculate f(3), f(4), f(5), f(6), f(7), and f(8).

Substitute 3 for n in [tex]\mathbf{f(n) = f(n-1)-f(n-2)}[/tex]

[tex]\mathbf{f(3) = f(3-1)-f(3-2)}[/tex]

[tex]\mathbf{f(3) = f(2)-f(1)}[/tex]

[tex]\mathbf{f(3) = 5-2}[/tex]

[tex]\mathbf{f(3) = 3}[/tex]

Following the above sequence, we have:

[tex]\mathbf{f(4) = f(3)-f(2)}[/tex]

[tex]\mathbf{f(4) = 3-5}[/tex]

[tex]\mathbf{f(4) = -2}[/tex]

[tex]\mathbf{f(5) = f(4)-f(3)}[/tex]

[tex]\mathbf{f(5) =-2- 3}[/tex]

[tex]\mathbf{f(5) = -5}[/tex]

[tex]\mathbf{f(6) = f(5)-f(4)}[/tex]

[tex]\mathbf{f(6) =-5- -2}[/tex]

[tex]\mathbf{f(6) = -3}[/tex]

[tex]\mathbf{f(7) = f(6)-f(5)}[/tex]

[tex]\mathbf{f(7) =-3--5}[/tex]

[tex]\mathbf{f(7) = 2}[/tex]

[tex]\mathbf{f(8) = f(7)-f(6)}[/tex]

[tex]\mathbf{f(8) =2--3}[/tex]

[tex]\mathbf{f(8) = 5}[/tex]

Hence, the values of f(3), f(4), f(5), f(6), f(7), and f(8) are 3, -2, -5, -3, 2, 5

Then, determine the value of f(25). ​

In (1), we have:

[tex]\mathbf{f(3) = 3}[/tex]

[tex]\mathbf{f(4) = -2}[/tex]

[tex]\mathbf{f(5) = -5}[/tex]

[tex]\mathbf{f(6) = -3}[/tex]

[tex]\mathbf{f(7) = 2}[/tex]

[tex]\mathbf{f(8) = 5}[/tex]

This means that:

[tex]\mathbf{f(n) = -f(n-3i)}[/tex]

Where i is greater than 0

Substitute 25 for n

[tex]\mathbf{f(25) = -f(25-3i)}[/tex]

Let i = 7.

So, we have:

[tex]\mathbf{f(25) = -f(25-3 \times 7)}[/tex]

[tex]\mathbf{f(25) = -f(25-21)}[/tex]

[tex]\mathbf{f(25) = -f(4)}[/tex]

So, we have:

[tex]\mathbf{f(25) = -(-2)}[/tex]

[tex]\mathbf{f(25) = 2}[/tex]

Hence, the value of f(25) is 2

Read more about sequence at:

https://brainly.com/question/9859279

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