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I need to find the $n$ of a geometric sequence, this formula is to find the $n$th term,

$n$th = $ar ^{n-1}$; so I need $n$ to be on the left instead of $n$th, I have all the other variables except for $n$. I want to know the position of a number in a geometric sequence, and $n$th stands for the number which I know already, also I know $a$ and $r$ already, but I don't know the position of my $n$th term, which is $^n$ .

For example ==> $[1, 2, 4, 8, 16]$ how can I get the position of $8$ for example, which should be 4 based on that sequence. Thanks

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    What ? I don't understand what do you need? – 2017-01-12
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    @openspace, I have edited my question, please check it out – 2017-01-12

1 Answers 1

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If $a_n = ar^{n-1}$ then $n = \log_r(a_n/a) + 1$.

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    thanks, but it's still confusing, as there is still an n on the right side – 2017-01-12
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    @SeyiAdekoya, $log_r(8/a)+1 = \cdots$. – 2017-01-12