Answer: [tex]a_n=3(-4)^{n-1}[/tex]
Step-by-step explanation:
Given sequence : [tex]3, -12, 48, -192, ...[/tex]
Here, First term [tex]a_1=3[/tex]
Second term [tex]a_2=-12[/tex]
and Ratio=[tex]r=\frac{a_2}{a_1}=\frac{-12}{3}=-4[/tex]
Third term [tex]a_3=48[/tex]
Ratio=[tex]r=\frac{a_3}{a_2}=\frac{48}{-12}=-4[/tex]
Fourth term [tex]a_4=-192[/tex]
Ratio=[tex]r=\frac{a_4}{a_3}=\frac{-192}{48}=-4[/tex]
Thus, the given sequence is geometric sequence with the common ratio r = -4.
The explicit rule for for the nth term in geometric sequence is given by
[tex]a_n=a_{1}r^{n-1}[/tex]
Then the explicit rule for the nth term of the given sequence will be :-
[tex]a_n=3(-4)^{n-1}[/tex]
