Respuesta :

The recursive formula for the geometric sequence is:

[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]

What is a geometric sequence?

  • A geometric sequence is a sequence in which the coefficient of consecutive terms is always the same, called common ratio q.

The recursive equation for a geometric sequence is:

[tex]f(n) = qf(n - 1)[/tex]

  • With f(1) as the first term.

In this problem, the sequence is: {-320, -80, -20, -5, . . .}

  • The first term is [tex]f(1) = -320[/tex].
  • The common ratio is [tex]q = \frac{-80}{-320} = \frac{1}{4}[/tex]

Hence, the recursive equation is:

[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]

You can learn more about geometric sequence at https://brainly.com/question/11847927

abidemiokin

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

Geometric progression

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

n the following sequence  -320, -80, -20, -5,...

The The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]is given as:

  • r = -80/-320 = -20/-80 = 1/4
  • The first term = -320

The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]

Learn more on geometric functions here: https://brainly.com/question/222209

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