Question

64, –48, 36, –27, ...

Which formula can be used to describe the sequence?

Answer 1

`\boxed{a_n \: = \: 64 \: * \: ( - (3)/(4) ) ^(n \: - \: 1) }`

Explanation:

• We first compute the ratio of this geometric sequence.

`r \: = \: ( - 48)/(64) \\ \\ r \: = \: (36)/( - 48) \\ \\ r \: = \: ( - 27)/(36)`

• We simplify the fractions:

`r \: = \: - (3 )/(4) \\ \\ r \: = \: - (3 )/(4) \\ \\ r \: = \: - (3 )/(4)`

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

`r \: = \: - (3 )/(4)`

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

`a_1 \: = \: 64; \: r \: = \: - (3 )/(4)`

We apply the data in this formula:

`\boxed{a_n \: = \: a_1 \: * \: {r}^( n \: - \: 1) }`

_______________________

We apply:

`\boxed {\bold{a_n \: = \: 64 \: * \: {( - (3)/(4) )}^( n \: - \: 1) }}`

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

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