Question

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128
Show work

Answer 1

first of what is the common ratio?

Answer 2

by what number do you multiply to obtain the next term?
(this number is called a 'common ratio' and denoted with r)

Answer 3

the first term, denoted as \(a_1\) and in this case, as you can see, it is -2.

Answer 4

So, all you need to do, is to fill the form below, for the first term and common ratio
\[\large a_n=a_{{\tiny~}_1} \left({\rm r} \right)^{n-1}\]

Answer 5

I am so confused

Answer 6

@Nnesha can you help please

Answer 7

okay first you need to find ( ratio)
geometric sequence mean when you get next term by dividing or multiplying previous term by something
so first term is -2 what you multiply with -2 to get next term which is 8 ?

Answer 8

i have no actual clue on how to do these. soooooo im guessing the next step would be like 8x4????

Answer 9

sorry to bother u but i have alot of questions i need help on today and your like the only person i know on here that actually helps me figure stuff out..

Answer 10

-2 times what = 8
8 times what = -32

Answer 11

-4?

Answer 12

-2x-2=8
8x-4=32
-32x4=128
???

Answer 13

i think i missed a - sign or two

Answer 14

yep right -4
\[\huge\rm 2 \times -4 =8\]
\[\huge\rm 8 \times -4 =-32\]
\[\huge\rm -32 \times -4 = 128\]

Answer 15

now plug r value into the formula that @((*-*)) gave you

Answer 16

r value?

Answer 17

\[\huge\rm a_n = a_1 \times r^{n-1}\]
r = ration
a_1 = is first term

Answer 18

r = ratio

Answer 19

now i feel dumb because i have no idea what a ratio is

Answer 20

ratio:t he common ratio is the ratio of a term to the previous term
http://www.regentsprep.org/regents/math/algtrig/atp2/geoseq.htm

Answer 21

does that mean the ratio is -2 and the common ratio is -4?

Answer 22

an= -2 x (-4) ^(n-1) is this correct?

Answer 23

yep right

Answer 24

no commone ratio is r
and -2 is first term

Answer 25

can you show me exactly how to write this on my home work and show all my work correctly

Answer 26

there is not a lot work to who
i already showed that how to find common ratio
then you just have to use formula to plug in a_1 and r values

Answer 27

show*

Answer 28

so i show my work like
-2x-2=8
8x-4=-32
-32x-4=128
an=-2x(-4)^(n-1)
or do i just write an=-2x(-4)^(n-1)

Answer 29

yep right looks good

Answer 30

thanks. is it okay to tag you in a few other questions later on? it should be just check my work questions.

Answer 31

sure :-)