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

`-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.}`

Answer 2

b)
`a_(n) = (-3)4^(n-1)`.

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 =
`(second term)/(first term)`

r =
`(-12)/(-3)` .

r = 4.

`a_(n) = (-3)4^(n-1)`.

Therefore,b)
`a_(n) = (-3)4^(n-1)`.