Given:
The given geometric sequence is 3, 12, 48, 192, ...
Required:
To find the 9th term in the given geometric sequence.
Explanation:
The first term is
[tex]a_1=3[/tex]Common ratio is
[tex]\begin{gathered} r=\frac{12}{3}=4 \\ \\ =\frac{48}{12}=4 \end{gathered}[/tex]The formula for nth term in geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]Here
[tex]\begin{gathered} a_9=3(4)^{9-1} \\ \\ =3\times4^8 \\ \\ =3\times65536 \\ \\ =196608 \end{gathered}[/tex]Final Answer:
The 9th term is 196608.
