Question

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

i need help on this problem

Answer 1

First find your r.

Answer 2

\[\frac{8}{-2} =~?\]\[\frac{-32}{8}=~?\]

Answer 3

...etc.

Answer 4

basically: \(\large\color{slate}{ r=(a_n ) \div (a_{n-1}) }\)

Answer 5

arithmetic sequence? or geometric sequence? @SolomonZelman

Answer 6

geometric

Answer 7

what do you mean, I am right!

Answer 8

Ok :) You had written arithmetic, haha

Answer 9

oh lol

Answer 10

so which one is right ?

Answer 11

\(\large\color{slate}{ a_n=a_1\times r^{n-1} }\)

Answer 12

do you see the common ratio?

Answer 13

Yeah... to find a common ratio, divide the preceding term by the one before it.

Answer 14

Make sure you first have a common ratio between all your terms.

Answer 15

i just dont know how to even start on this problem. like im horrible in math

Answer 16

Find your ratio first. \(\color{blue}{\text{Originally Posted by}}\) @Jhannybean
\[\frac{8}{-2} =~?\]\[\frac{-32}{8}=~?\]
\(\color{blue}{\text{End of Quote}}\)

Answer 17

use anything for "r" :

\(\large\color{slate}{ r=(8) \div (-2) }\)
\(\large\color{slate}{ r=(-32) \div (8) }\)
\(\large\color{slate}{ r=(128) \div (-32) }\)

see how I am dividing a term, by the one before to find r?

this is denoted as: \(\large\color{slate}{ r=(a_n) \div (a_{n-1}) }\)

Answer 18

just wondering if anyone explained the common ratio here?

Answer 19

common ratio, if anyone didn't know: is a number by which you multiply a term, to find the term right after

Answer 20

The common ratio is the term that you find that is the same for each pair in the sequence.

Answer 21

That is why we are asking you to find the common rati between each pair of terms.

Answer 22

@Jhannybean I see you did

Answer 23

Elizabeth, lost?

Answer 24

Perhaps as Einstein said "make it simple, but no simpler"

Answer 25

first need to find the common ratio

Answer 26

Elizabeth, do you want me to explain everything very thoroughly?

Answer 27

@SolomonZelman is the ideal person to explain

Answer 28

that is debatable... I wouldn't necessarily say that, whether I hold like that or not.
Although I will certainly attempt my best!

Answer 29

Elizabeth, say something, please

Answer 30

So @elizabeth710 ? Are you still here?

Answer 31

yes im here

Answer 32

okay, will start from this:

Do you understand what the notations I will write in blue mean?
\(\large\color{blue}{ a_1 }\) , \(\large\color{blue}{ a_2 }\) , \(\large\color{blue}{ a_3 }\)
\(\large\color{blue}{ r }\) , \(\large\color{blue}{ a_n }\)

Answer 33

sadly no :/

Answer 34

What do you mean by your second line?

Answer 35

got disconnected-:(

Answer 36

Okay,

so say you have the following sequence:
\(\large\color{brown}{ 1,~3,~9,~27~... }\)

Answer 37

So
\(\large\color{brown}{ 1 }\) is the first term, denoted as \(\large\color{brown}{ a_1 }\) .
\(\large\color{brown}{ 3 }\) is the 2nd term, denoted as \(\large\color{brown}{ a_2 }\) .
\(\large\color{brown}{ 9 }\) is the 3rd term, denoted as \(\large\color{brown}{ a_3 }\) .
\(\large\color{brown}{ 27 }\) is the 4th term, denoted as \(\large\color{brown}{ a_4 }\) .

Answer 38

and on... see ?

So, can you explain to me, what would \(\large\color{brown}{" a_5" }\) mean?

Answer 39

Elizabeth, if you are not getting what I am saying, please say so...

Answer 40

okay, between each term of a geometric sequence is what we call a "common ratio"

Answer 41

the reason we call it a common ratio is becuase if you divide the next term, by the previous term, you will have a ratio which is "common"

Answer 42

i.e divide 8 by -2 = -4, then divide -32 by 8 = -4

Answer 43

This is what @SolomonZelman is trying to explain to you

Answer 44

i got a_n=-2×-4