What is the recursive formula for the geometric sequence with this explicit formula an= 5 * (-1/8)^(n-1)

[tex] a_n=5\left(-\dfrac{1}{8}\right)^{n-1}\\\\a_1=5\left(-\dfrac{1}{8}\right)^{1-1}=5\left(-\dfrac{1}{8}\right)^0=5\\\\\text{The recursive formula:}\\\\a_n=\left\{\begin{array}{ccc}a_1=5\\a_{n+1}=-\dfrac{1}{8}a_{n}\end{array}\right [/tex]

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psm22415 psm22415 · Answer 2 · 2022-01-19T04:59:17+01:00

The recursive formula for the geometric sequence is [tex]\rm a_n_+_1= \dfrac{-1}{8}a_n[/tex].

Given that

The geometric sequence with this explicit formula;

[tex]\rm a_n= 5\times \dfrac{-1}{8}^{(n-1)}[/tex]

We have to determine

The recursive formula for the geometric sequence.

According to the question

The recursive formula for the geometric sequence is determined in the following steps given below.

The geometric sequence with this explicit formula;

[tex]\rm a_n= 5\times \dfrac{-1}{8}^{(n-1)}[/tex]

Then,

For the recursive formula substitute n= 1,

[tex]\rm a_n= 5\times \dfrac{-1}{8}^{(n-1)}\\\\\rm a_1= 5\times \dfrac{-1}{8}^{(1-1)}\\\\\rm a_1= 5\times \dfrac{-1}{8}^0\\\\\rm a_1= 5\times 1\\\\\rm a_1= 5[/tex]

Therefore,

The recursive formula for the geometric sequence is,

[tex]a_n_+_1= \dfrac{-1}{8}a_n[/tex]

Hence, the recursive formula for the geometric sequence is [tex]\rm a_n_+_1= \dfrac{-1}{8}a_n[/tex].

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