Question

64, –48, 36, –27, ... Which formula can be used to describe the sequence?

Answer 1

Answer:

$\boxed{a_n \: = \: 64 \: \times \: ( - \frac{3}{4} ) ^{n \: - \: 1} }$

Step-by-step explanation:

• We first compute the ratio of this geometric sequence.

$r \: = \: \frac{ - 48}{64} \\ \\ r \: = \: \frac{36}{ - 48} \\ \\ r \: = \: \frac{ - 27}{36}$

• We simplify the fractions:

$r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4} \\ \\ r \: = \: - \frac{3 }{4}$

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

$r \: = \: - \frac{3 }{4}$

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

$a_1 \: = \: 64; \: r \: = \: - \frac{3 }{4}$

We apply the data in this formula:

$\boxed{a_n \: = \: a_1 \: \times \: {r}^{ n \: - \: 1} }$

_______________________

We apply:

$\boxed {\bold{a_n \: = \: 64 \: \times \: {( - \frac{3}{4} )}^{ n \: - \: 1} }}$

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

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