Monique deposited her money in the bank to collect interest. The first month, she had $275 in her account. After the sixth month, she had $303.62 in her account. Use sequence notation to represent the geometric function. an = 275 ⋅ (1.02)n−1 an = 275 ⋅ (0.10)n−1 an = 303.62 ⋅ (1.02)n−1 an = 303.62 ⋅ (1.10)n−1

Answer:[tex]a_n = 275(1.02)^{n - 1} [/tex]Step-by-step explanation:The geometric sequence is given explicitly by the formula:[tex]a_n = a(r)^{n - 1} [/tex]In the first month, Monique had $275 in her account.[tex] \implies \: a = 275[/tex]After the sixth month, she had $303.62 in her account.[tex]a_6 = 303.62[/tex][tex] \implies \: a {r}^{5} = 303.62[/tex]We solve for r, [tex] \frac{a {r}^{5} }{a} = \frac{303.62}{275} [/tex][tex] \implies \: r = ( \frac{303.62}{275} )^{ \frac{1}{5} } = 1.02[/tex]We fix everything back into the original formula to get:[tex]a_n = 275(1.02)^{n - 1} [/tex]