–81, 108, –144, 192, ...

Which formula can be used to describe the sequence?

f(x) = –81(four-thirds) Superscript x minus 1
f(x) = –81(negative three-fourths) Superscript x minus 1
f(x) = –81(negative four-thirds) Superscript x minus 1
f(x) = –81(three-fourths) Superscript x minus 1

The formula which can be used to describe the sequence is:

⇒ 3rd answer

Step-by-step explanation:

The terms of the sequence are -81, 108, -144, 192, ...

∵ 108 ÷ -81 =

∵ -144 ÷ 108 =

∵ 192 ÷ -144 =  

- There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

The formula of the nth term of the geometric sequence is , where a is the first term and r is the constant ratio between each two consecutive terms

∵ The first term is -81

∴ a = -81

∵ The constant ratio =  

∴ r =  

- Substitute then in the formula above

∴  

Assume that = f(x)

∴ n = x

∴  

The formula which can be used to describe the sequence is:

here

step-by-step explanation: