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Nady [450]
3 years ago
14

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

Mathematics
2 answers:
Troyanec [42]3 years ago
6 0

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.







Komok [63]3 years ago
5 0

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




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