Which formula can be used to describe the sequence? Negative two-thirds, −4, −24, −144,... fx = 6negative two-thirds Superscript x minus 1 fx = −6Two-thirds Superscript x minus 1 fx = Negative two-thirds6x − 1 fx = Two-thirds−6x − 1

Answer: ƒ(x) = -⅔(6)ˣ⁻¹Your 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 seriesThe 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.