## Question

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

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

## Answers

#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.

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