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Use a recursive function for the geometric sequence 2, −8, 32, −128, … to represent the 9th term.

A. f(9) = f(1) + −4(8)
B. f(9) = f(8) + −4(8)
C. f(9) = f(1) • (−4)8
D. f(9) = f(8) • (−4)

Respuesta :

sqdancefan

Answer:

  D.  f(9) = f(8) • (−4)

Step-by-step explanation:

The common ratio for this geometric sequence is -8/2 = -4, so the 9th term is -4 times the 8th term:

  f(9) = -4·f(8) . . . . . matches choice D

Answer:

Option D.

Step-by-step explanation:

The given geometric sequence is

2, −8, 32, −128, …

Here first term is 2 and common ratio is

[tex]\text{Common ratio}=\dfrac{-8}{2}=-4[/tex]

The recursive formula for a GP is

[tex]f(n)=f(n-1)\cdot r[/tex]

where, r is common ratio.

We need to find the recursive function to represent the 9th term.

Substitute n=9 and r=-4 in the above function.

[tex]f(9)=f(9-1)\cdot (-4)[/tex]

[tex]f(9)=f(8)\cdot (-4)[/tex]

Therefore, the correct option is D.

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