Answer:
[tex]T_n = -48* (-\frac{1}{2})^{n}[/tex]
Step-by-step explanation:
Given
[tex]24, -12, 6,...[/tex]
Required
Write a formula
The above sequence shows a geometric sequence because:
[tex]r = \frac{-12}{24} = \frac{6}{-12} = -\frac{1}{2}[/tex] -- common ratio
The equation is determined using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 24[/tex]
Substitute values for a and r
[tex]T_n = 24* (-\frac{1}{2})^{n-1}[/tex]
Apply law of indices:
[tex]T_n = 24* (-\frac{1}{2})^{n} * (-\frac{1}{2})^{-1}[/tex]
[tex]T_n = 24* (-\frac{1}{2})^{n} * 1/(-\frac{1}{2})[/tex]
[tex]T_n = 24* (-\frac{1}{2})^{n} * 1*-2[/tex]
[tex]T_n = 1*-2*24* (-\frac{1}{2})^{n}[/tex]
[tex]T_n = -48* (-\frac{1}{2})^{n}[/tex]
The above represents the explicit formula
