## –81, 108, –144, 192, … Which formula can be used to describe the sequence? f(x) = –81(four-thirds) Superscript x m

Question

–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

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3 weeks 2021-09-28T02:57:06+00:00 2 Answers 0

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: 