How do you find a formula for the nth term of the geometric sequence: 8, 12, 18, 27, ...?

#n#th term is #8*(3/2)^(n-1)#

Explanation:

The formula for #n#th term of geometric sequence is #a_1q^(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=a_k/a_(k-1)=a_2/a_1=12/8=3/2# for any #k>1#.

Moreover

#12/8=18/12=27/18=...#

so the sequence is geometric indeed.

...

Fun fact: next term is not an integer.