Question

find an equation for the nth term of the sequence. -3, -12, -48, -192, ... select one: a. an = 4 • -3n 1 b. an = -3 • 4n - 1 c. an = -3 • 4n d. an = 4 • -3n

Answer 1

Answer:

b)  $a_{n} = (-3)4^{n-1}$.

Step-by-step explanation:

Given :  -3, -12, -48, -192, ...

To find : find an equation for the nth term of the sequence.

Solution : We have given  -3, -12, -48, -192, ...

Nth term of geometric sequence = $a_{n} = a_{1}r^{n-1}$.

Where, $a_{n}= nth terms$.

$a_{1}= first term$.

r = common ratio.

r = $\frac{second term}{first term}$

r =  $\frac{-12}{-3}$ .

r = 4.

$a_{n} = (-3)4^{n-1}$.

Therefore,b)  $a_{n} = (-3)4^{n-1}$.

Answer 2

$-3;-12;-48;-192;...\\\\It's\ the\ geometric\ sequence:a_n=a_1r^{n-1}\\\\a_1=-3;\ a_2=-12\\\\r=a_2:a_1\to r=-12:(-3)=4\\\\\boxed{a_n=-3\cdot4^{n-1}}\to\fbox{b.}$