Geometric Sequence
The general term of a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]Where a1 is the first term, r is the common ratio and an is the nth term.
We are given the sequence 2, -8, 32, ....
The first term is a1=2. The common ratio can be found by dividing two consecutive terms:
[tex]r=\frac{-8}{2}=-4[/tex]If we use the following terms:
[tex]r=\frac{32}{-8}=-4[/tex]This verifies we were given a correct geometric sequence.
We are required to find the term n=12, so we substitute in the general form:
[tex]a_{12}=2\cdot(-4)^{11}=2\cdot(-4194304)=-8388608[/tex]The 12th term is -8388608
