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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

Respuesta :

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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]

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