Question

Write an explicit formula for the An, and the n^th term of the sequence 24,-12,6,....

Answer 1

Answer:

$T_n = -48* (-\frac{1}{2})^{n}$

Step-by-step explanation:

Given

$24, -12, 6,...$

Required

Write a formula

The above sequence shows a geometric sequence because:

$r = \frac{-12}{24} = \frac{6}{-12} = -\frac{1}{2}$ -- common ratio

The equation is determined using:

$T_n = ar^{n-1}$

Where

$a = 24$

Substitute values for a and r

$T_n = 24* (-\frac{1}{2})^{n-1}$

Apply law of indices:

$T_n = 24* (-\frac{1}{2})^{n} * (-\frac{1}{2})^{-1}$

$T_n = 24* (-\frac{1}{2})^{n} * 1/(-\frac{1}{2})$

$T_n = 24* (-\frac{1}{2})^{n} * 1*-2$

$T_n = 1*-2*24* (-\frac{1}{2})^{n}$

$T_n = -48* (-\frac{1}{2})^{n}$

The above represents the explicit formula