Use the geometric series formulas to find the sum of the geometric series.1 + √3 + 3 + 3√3 + ⋯ + 243

Answer:573.578Step-by-step explanation:Geometric Sequence is the sequence in which every digit is the same multiplier of its previous digit.The given Sequence is: √3 + 3 + 3√3 + ⋯ + 243here a₁ = √3, r = 3 ÷ √3 = √3.First we will find the number of terms for this we use formula:[tex]a_{n} = a_{1}(r)^{n-1}[/tex]⇒ 243 = √3(√3)ⁿ⁻¹   ⇒ (√3)¹⁰ = √3(√3)ⁿ⁻¹⇒ (√3)⁹ = (√3)ⁿ⁻¹⇒ n - 1 = 9⇒ n = 10The formula of sum of geometric series is:[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]⇒ [tex]S_n=\frac{\sqrt{3}(1-\sqrt{3}^{10})}{1-\sqrt{3}}[/tex]⇒ Sₙ = 572.578147716Thus the sum of 1 + √3 + 3 + 3√3 + ⋯ + 243 = 1 + 572.578 = 573.578