Question

Which formula can be used to describe the sequence? Negative two-thirds, −4, −24, −144,... f(x) = 6(negative two-thirds) Superscript x minus 1 f(x) = −6(Two-thirds) Superscript x minus 1 f(x) = Negative two-thirds(6)x − 1 f(x) = Two-thirds(−6)x − 1

Answer 1

Answer:

b

Step-by-step explanation:

Answer 2

Answer:

ƒ(x) = -⅔(6)ˣ⁻¹

Step-by-step explanation:

Your geometric series  is

-⅔, -4, -24, -144 …

The formula for the nth term of a geometric series is

aₙ = a₁rⁿ⁻¹

1. Calculate the common ratio (r)

$\dfrac{a_{2}}{ a_{1}}= \dfrac{-4}{-2/3}} = 4 \times \dfrac{3}{2} = 6\\\\\dfrac{a_{3}}{ a_{2}}= \dfrac{-24}{-4} = 6\\\\\dfrac{a_{4}}{ a_{3}}= \dfrac{-144}{-24} = 6$

The common ratio is 6.

2. Write the formula for the series

The formula for the nth term is

aₙ = -⅔(6)ⁿ⁻¹ or  

ƒ(x) = -⅔(6)ˣ⁻¹

Check:

a₁ = -⅔(6)⁰ = -⅔ ×    1 = -      ⅔

a₂ = -⅔(6)¹ = -⅔ ×    6 = -    4

a₃ = -⅔(6)² = -⅔ ×  36 = - 24

a₄ = -⅔(6)³ = -⅔ × 216 = -144

It checks.