Answer :
Sequence a: 4, 8, 12, 16, 20, ...
As you can observe, this is an arithmetic sequence with a difference of 4 because each new term is 4 units more than the previous one: 4+4=8, 8+4=12, 12+4=16,...
We have to use the function for arithmetic sequences
[tex]f(n)=f(1)+(n-1)\cdot d[/tex]Where f(1) = 4 and d = 4. So, the function is
[tex]f(n)=4+(n-1)\cdot4=4+4n-4=4n[/tex]Hence, the function of the sequence a is f(n) = 4n.
Sequence b: 1, 4, 16, 64, 256, ...
This sequence is geometric because each new term is four times its previous one: 1x4=4, 4x4=16, 16x4=64,...
We have to use the function for geometric sequences
[tex]f(n)=f(1)\cdot r^{n-1}_{}[/tex]Where f(1) = 1 and r = 4.
[tex]f(n)=1\cdot(4)^{n-1}[/tex]Hence, the function is
[tex]f(n)=4^{n-1}[/tex]Sequence c.
As you can observe, this sequence is formed by the same number, which means it represents a constant function like the following
[tex]f(n)=\sqrt[]{3}[/tex]