Question

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

Answer 1

missing terms of the geometric series are

-768,192,-48

and

768,192. 48

.Explanation:

we know that general formula of geometric progression is

`an =a.r^(n-1)`...........(1)

we are given

a2=3072

a6=12

we have to find

a3=?

a4=?

a5=?

by equayion (1)

`a 2=a.r^(2-1)`

3072=a.r

similarly

`a6=a.r^(6-1)`

`12=a.r^(6-1)`

12=a.r*(5)

`(a.r^(5) )/(a.r)`=12/3072

`\sqrt r^(4) =\sqrt{(1)/(256) }`

r=±1/4

first put

r=1/4

a3=a2r

a3=3072/4=768

a4=a2.r^2

a4=3072/16

a4=192

a5=a2.r^3

a5=3072/64

a5=48

but for

r= -1/4

a3=a2r

a3=3072/4=-768

a4=a2.r^2

a4=3072/16

a4=192

a5=a2.r^3

a5=3072/64

a5= -48

Answer 2

The missing terms of the geometric series are

A.
`-768,192,-48`

and

B.
`768,192,48`

Explanation:

The given geometric sequence is
`...,3072,?,?,12,...`.

The second and sixth term of the geometric sequence are
`3072` and
`12` respectively.

Recall that the nth term of a geometric sequence is given by,

`t_n=ar^(n-1)`.

This implies that the second term will be,

`3072=ar^(2-1)`.

`\Rightarrow 3072=ar---(1)`.

Also the 6th term is

`12=ar^(6-1)`.

`12=ar^(5)---(2)`.

We divide equation (2) by (1) to get,

`(ar^5)/(ar)=(12)/(3072)`

`\Rightarrow r^4=(1)/(256)`

`\Rightarrow r=\pm \sqrt[4]{(1)/(256) }`

`r=\pm (1)/(4)`

If

`r=(1)/(4)`

We get,

`t_3=3072*(1)/(4) =768`

`t_4=768*(1)/(4) =192`

`t_5=192*(1)/(4) =48`

But If

`r=-(1)/(4)`

We get,

`t_3=3072*(-1)/(4) =-768`

`t_4=-768*(-1)/(4) =192`

`t_5=192*(-1)/(4) =-48`

Therefore the correct answer is A and B.