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Answer:
[tex]T_n =-\frac{8}{3} (-3)^{n}[/tex]
Step-by-step explanation:
Given
[tex]Sequence: 8, -24, 72[/tex]
Required
Determine the n term
The above sequence is geometric. So, we calculate the common ratio first:
[tex]r = \frac{T_2}{T_1}[/tex]
[tex]r = \frac{-24}{8}[/tex]
[tex]r = -3[/tex]
The equation is then calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = T_1 = 8[/tex]
and
[tex]r = -3[/tex]
The equation becomes:
[tex]T_n =8 * (-3)^{n-1}[/tex]
Apply law of indices:
[tex]T_n =8 * (-3)^{n} * (-3)^{-1}[/tex]
[tex]T_n =8 * (-3)^{n} * \frac{1}{-3}[/tex]
[tex]T_n =-8 * (-3)^{n} * \frac{1}{3}[/tex]
[tex]T_n =-\frac{8}{3} * (-3)^{n}[/tex]
[tex]T_n =-\frac{8}{3} (-3)^{n}[/tex]