Step-by-step explanation:
a geometric sequence is s sequence, where every new element is generated by multiplying the previous element by the same number.
a n = a1 × number^(n-1)
so, a12/a7 = number^5
=> 2187/9 = 243 = number^5
=>
[tex]number = \sqrt[5]{243} [/tex]
=> number = 3
so, what is a1 ?
it has to satisfy e.g. a7.
9 = a1 × 3^6
9 = 3^2
=> 3^2 = a1 × 3^6
=> 1 = a1 × 3^4
=> a1 = 1/(3^4) = 1/81
therefore, the whole formula is
a n = 1/81 × 3^(n-1 )
