Answer:
The recursive formula is
[tex]a_n=2a_{n-1}[/tex]
and the explicit formula is
[tex]a_n=6\cdot 2^{n-1}[/tex]
Step-by-step explanation:
Given the sequence 6, 12, 24, 48.
In this sequence,
[tex]a_1=6\\ \\a_2=12\\ \\a_3=24\\ \\a_4=48[/tex]
Note that
[tex]12=2\cdot 6\Rightarrow a_2=2\cdot a_1\\ \\24=2\cdot 12\Rightarrow a_3=2\cdot a_2\\ \\48=2\cdot 24\Rightarrow a_4=2\cdot a_3[/tex]
Hence, the recursive formula is
[tex]a_n=2a_{n-1}[/tex]
and the explicit formula is
[tex]a_n=2^{n-1}\cdot a_1\\ \\a_n=6\cdot 2^{n-1}[/tex]
