Answered

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Write an explicit formula for the nth term or the sequence 8,-24, 72

Sagot :

MrRoyal

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]

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