find the 12th term of the geometric sequence 1,3,9,...
we have
a1=1 ------> first term
a2=3
a3=9
Find the value of r (common ratio)
we have that
a2/a1=3/1=3
a3/a2=9/3=3
so
the common ratio is
r=3
we know that the general equation for a geometric sequence is
[tex]a_n=a_1\cdot r^{(n-1)}[/tex]we have
a1=1
r=3
substitute
[tex]\begin{gathered} a_n=1\cdot3^{(n-1)} \\ a_n=3^{(n-1)} \end{gathered}[/tex]Find the 12th term
so
For n=12
substitute in the equation
[tex]\begin{gathered} a_{12}=3^{(12-1)} \\ a_{12}=3^{(11)} \\ a_{12}=177,147 \end{gathered}[/tex]therefore
