Question

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

Answer 1

Answer:

$T_n =-\frac{8}{3} (-3)^{n}$

Step-by-step explanation:

Given

$Sequence: 8, -24, 72$

Required

Determine the n term

The above sequence is geometric. So, we calculate the common ratio first:

$r = \frac{T_2}{T_1}$

$r = \frac{-24}{8}$

$r = -3$

The equation is then calculated using:

$T_n = ar^{n-1}$

Where

$a = T_1 = 8$

and

$r = -3$

The equation becomes:

$T_n =8 * (-3)^{n-1}$

Apply law of indices:

$T_n =8 * (-3)^{n} * (-3)^{-1}$

$T_n =8 * (-3)^{n} * \frac{1}{-3}$

$T_n =-8 * (-3)^{n} * \frac{1}{3}$

$T_n =-\frac{8}{3} * (-3)^{n}$

$T_n =-\frac{8}{3} (-3)^{n}$