Answer:
[tex]a_6=-384[/tex]
Step-by-step explanation:
The [tex]n^{th}[/tex] term of the sequence is given as [tex]a_n=-3\cdot 2^{n+1}[/tex].
To find the sixth term, which is denoted by [tex]a_6[/tex], we substitute n=6 into the given rule.
This will give us:
[tex]a_6=-3\cdot 2^{6+1}[/tex]
Simplify the exponent to get:
[tex]a_6=-3\cdot 2^{7}[/tex]
We simplify further to get:
[tex]a_6=-3\cdot 128[/tex]
This simplifies to
[tex]a_6=-384[/tex]
