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Determine if the sequence is algebraic or geometric, and find the common difference or ratio.

x 1 2 3 4
f(x) 3 9 27 81

A.) Algebraic, common difference = 3
B.) Algebraic, common difference = 6
C.) Geometric, common ratio = 3
D.) Geometric, common ration = 6

Respuesta :

calculista

Answer:

Option C.) Geometric, common ratio = 3

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant

The constant is called the common ratio

In this problem we have

For x=1, f(1)=3

For x=2, f(2)=9

For x=3, f(3)=27

For x=4, f(4)=81

so

f(2)/f(1)=9/3=3 -----> f(2)=3*f(1)

f(3)/f(2)=27/9=3 -----> f(3)=3*f(2)

f(4)/f(3)=81/27=3 -----> f(4)=3*f(3)

f(n+1)/f(n)=3 -----> f(n+1)=3*f(n)

therefore

This is a Geometric sequence and the common ratio is equal to 3

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