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The fifth term of a geometric sequence is 781.25. Each previous term is 1/5 of the value of the current term. Which recursive formula represents the situation?

Respuesta :

Answer:

[tex]a_n=5a_{n-1}[/tex]

Step-by-step explanation:

Given fifth term of a geometric sequence is 781.25.

[tex]a_5= 781.25[/tex].

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

[tex]a_n=ra_{n-1}[/tex]

Plugging value of r in above formula, we get

[tex]a_n=5a_{n-1}[/tex]

Therefore, recursive formula would be  [tex]a_n=5a_{n-1}[/tex] represents the situation.

abidemiokin

The required recursive function is an = 5an-1

Recursive function

Let the general formula for the recursive function be expressed as:

  • an = Ran-1

where

  • R is the common ratio

If the fifth term is 781.25, hence a5 = 781.25

If the previous term is 1/5 of the value of the current term.

Hence R = 5

Substitute the given values into the formula:

781.25 = 5an-1

Hence the required recursive function is an = 5an-1

Learn more on recursive function here: https://brainly.com/question/11316313

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