ANSWER
[tex]a_n=24\mleft(\frac{1}{2}\mright)^{n-1}[/tex]
EXPLANATION
The generic formula for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
a is the first term of the sequence:
[tex]\begin{gathered} a_1=ar^{1-1} \\ a_1=ar^0 \\ a_1=a \end{gathered}[/tex]
Therefore, a = 24.
Then, with the second term we can find r:
[tex]\begin{gathered} a_2=24r^{2-1} \\ 12=24r \\ r=\frac{12}{24} \\ r=\frac{1}{2} \end{gathered}[/tex]
The explicit formula for this sequence is:
[tex]a_n=24\mleft(\frac{1}{2}\mright)^{n-1}[/tex]
