Question

Calculate the missing terms of the geometric sequence ...,3072, 7,2,7, 12,.... Select all that apply.

Answer 1

The missing terms are 768, 192, 48.

Explanation:

From the given geometric sequence

First term= a_1=3072

Fifth Term= a_5=12

The general form of a geometric sequence is:

a_n=ar^(n-1)

here a_nis the nth term, a is the first term and r is the common ratio.

We will use the general form for term 5 to calculate the value of r.

So the general form for term 5 will be

a_5=3072* r^(5-1)

Putting the value of a_5

12=3072* r^4

r^4= 12/3072

r^4= 1/256

r^4= 1/[(4)^4]

Solving for r

r= 1/4

Now

a_2= ar^(2-1)

a_2=3072*r

a_2=3072* 1/4

a_2=768

a_3= ar^(3-1)

a_3=3072*r^2

a_3=3072*(1/4)^2

a_3=3072* 1/16

a_3=192

a_4= ar^(4-1)

a_4=3072*r^3

a_4=3072*(1/4)^3

a_4=3072* 1/64

a_4=48