Respuesta :

MissSpanish

Answer:

[tex] \boxed{a_n \: = \: 64 \: \times \: ( - \frac{3}{4} ) ^{n \: - \: 1} }[/tex]

Step-by-step explanation:

  • We first compute the ratio of this geometric sequence.

[tex]r \: = \: \frac{ - 48}{64} \\ \\ r \: = \: \frac{36}{ - 48} \\ \\ r \: = \: \frac{ - 27}{36} [/tex]

  • We simplify the fractions:

[tex]r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4}[/tex]

  • We deduce that it is the common ratio because it is the same between each pair.

[tex]r \: = \: - \frac{3 }{4}[/tex]

  • We use the first term and the common ratio to describe the equation:

[tex]a_1 \: = \: 64; \: r \: = \: - \frac{3 }{4}[/tex]

We apply the data in this formula:

[tex] \boxed{a_n \: = \: a_1 \: \times \: {r}^{ n \: - \: 1} }[/tex]

_______________________

We apply:

[tex] \boxed {\bold{a_n \: = \: 64 \: \times \: {( - \frac{3}{4} )}^{ n \: - \: 1} }}[/tex]

Data: The unknown "n" is the term you want

MissSpanish

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