Find a formula for the nth term of the geometric sequence: 8, 12, 18, 27, ...

Find a formula for the nth term of the geometric sequence: 8, 12, 18, 27, ...
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bibliothecaqz
The formula for nth term of geometric sequence is ${a}_{1}{q}^{n-1}$, where ${a}_{1}$ is the 1st term and q is the quotient of this sequence (check for n=1).
To find quotien q we must divide any term by its previous one - result will be the same (it's geometric sequence definition).
$q=\frac{{a}_{k}}{{a}_{k-1}}=\frac{{a}_{2}}{{a}_{1}}=\frac{12}{8}=\frac{3}{2}$ for any k>1.
Moreover
$\frac{12}{8}=\frac{18}{12}=\frac{27}{18}=...$
so the sequence is geometric indeed.