Question

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

Answer 1

Answer:

The missing terms of the geometric series are

A. $-768,192,-48$

and

B. $768,192,48$

Step-by-step 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,

$\frac{ar^5}{ar}=\frac{12}{3072}$

$\Rightarrow r^4=\frac{1}{256}$

$\Rightarrow r=\pm \sqrt[4]{\frac{1}{256} }$

$r=\pm \frac{1}{4}$

If

$r=\frac{1}{4}$

We get,

$t_3=3072\times\frac{1}{4} =768$

$t_4=768\times\frac{1}{4} =192$

$t_5=192\times\frac{1}{4} =48$

But If

$r=-\frac{1}{4}$

We get,

$t_3=3072\times\frac{-1}{4} =-768$

$t_4=-768\times\frac{-1}{4} =192$

$t_5=192\times\frac{-1}{4} =-48$

Therefore the correct answer is A and B.

Answer 2

Answer:

missing terms of the geometric series are

-768,192,-48

and

768,192. 48

.Step-by-step 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)

$\frac{a.r^{5} }{a.r}$=12/3072

$\sqrt r^{4} =\sqrt{\frac{1}{256} }$

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