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

1 Answer
Mar 9, 2016

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

Explanation:

The formula for nth 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.