Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.

Answer:[tex]a_n = 4.5 * 3^{n-1}[/tex]Step-by-step explanation:Given[tex]a_4 = 121.5[/tex][tex]r = 3[/tex]Required[tex]a_n = a_1 * r^{n -1}[/tex]Substitute 4 for n in [tex]a_n = a_1 * r^{n -1}[/tex][tex]a_4 = a_1 * r^{4 -1}[/tex][tex]a_4 = a_1 * r^3[/tex]Substitute 121.5 for [tex]a_4[/tex][tex]121.5 = a_1 * 3^3[/tex][tex]121.5 = a_1 * 27[/tex]Solve for a1[tex]a_1 = \frac{121.5}{27}[/tex][tex]a_1 = 4.5[/tex]So, we have:[tex]a_n = a_1 * r^{n -1}[/tex][tex]a_n = 4.5 * 3^{n-1}[/tex]