Given
The sequence,
6, 24, 96, 384.
To find the nth term of the sequence.
Explanation:
It is given that,
The sequence is,
6, 24, 96, 384.
That implies,
[tex]\frac{24}{6}=\frac{96}{24}=\frac{384}{96}=4[/tex]Then, the given sequence is a GP.
Therefore,
The nth term of the given sequence is,
[tex]\begin{gathered} a_n=ar^{n-1} \\ =6(4)^{n-1} \end{gathered}[/tex]That implies,
[tex]\begin{gathered} a_7=ar^{7-1} \\ =6(4)^6 \\ =6\times4096 \\ =24576 \end{gathered}[/tex]Hence, the seventh term of the sequence is 24576.