Question

What is the sum of the geometric sequence -3, 18, -108, ... if there are 8 terms?

719,835
119,973
-119,973
-719,835

Answer 1

@jdoe0001

Answer 2

any ideas on the common ratio? that is, "r"

Answer 3

um..not really :/

Answer 4

hmmm do you know what a geometric sequence is?

Answer 5

yes

Answer 6

well... to get the next term... .you'd multiply by "something" the current term

notice say from -3 to 18
-3 * something = 18

so... that "something" is the common ratio, or "r"

which is the same used to get -108
that is 18 * something = -108

Answer 7

oh okay I do I find the 8th term?

Answer 8

wait if I find the rule can I find the sum..

Answer 9

let me find the rule..

Answer 10

\(\Large \bf a_{\color{brown}{ n}}=a_1\cdot r{\color{blue}{ }}^{{\color{brown}{ n}}-1}\implies
a_{\color{brown}{ 8}}=a_1\cdot r{\color{blue}{ }}^{{\color{brown}{ 8}}-1}\)

Answer 11

yes I got the rule as (-3)(-6)^(n-1)

Answer 12

yeap so the 8th term is \(\bf a_{\color{brown}{ 8}}=-3\cdot -6^{{\color{brown}{ 8}}-1}\)

Answer 13

now the sum of the first 8 terms, will be \(\Large \bf S_{\color{brown}{ 8}}=a_1\left(\cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}}\right)\)

Answer 14

anyhow \(\bf S_{\color{brown}{ n}}=a_1\left(\cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}}\right)\)

Answer 15

so.. can't we find each of the terms and find the sum of those all..

Answer 16

you could do that, yes
or you could just use the 1st term and the 8th term, and use \(\bf S_{\color{brown}{ n}}=a_1\left(\cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}}\right)\)

Answer 17

well... I take that back... no the 8th term, but the common ratio "r" rather

Answer 18

okay... so: =-3(1- ?) / (1-?)

Answer 19

I don't really know the ? marks..

Answer 20

what is r ?

Answer 21

well... you already know what "r" is, is -6 that's the common ratio
or what you used to get from -3 to 18 and from 18 to -108 so

\(\bf S_{\color{brown}{ n}}=a_1\left(\cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}}\right)\implies S_{\color{brown}{ 8}}=-3\left(\cfrac{1-{\color{blue}{ (-6)}}^{\color{brown}{ 8}}}{1-{\color{blue}{ (-6)}}}\right)\)

Answer 22

oh yeah... I keep getting 859,803

Answer 23

\(\bf S_{\color{brown}{ 8}}=-3\left(\cfrac{1-{\color{blue}{ (-6)}}^{\color{brown}{ 8}}}{1-{\color{blue}{ (-6)}}}\right)\implies
S_{\color{brown}{ 8}}=-3\left(\cfrac{1-1679616}{7}\right)\)

Answer 24

yes that's what I got.

Answer 25

859,803 ?

Answer 26

yeap

Answer 27

heheh.... hmmm w0t?

Answer 28

lol do you know ;)

Answer 29

ok... so.... what's 1-1679616?

Answer 30

it's -1679615

Answer 31

yeap.... so dividing that by 7... won't give you 859,803 though

Answer 32

yes that would give you -239945 and when you multiply that by -3 you would get 859,803

Answer 33

hmmm

Answer 34

;)

Answer 35

hmm I see... pemdas got us =)

Answer 36

ohh

Answer 37

\(\bf S_{\color{brown}{ 8}}=-3\left(\cfrac{1-{\color{blue}{ (-6)}}^{\color{brown}{ 8}}}{1-{\color{blue}{ (-6)}}}\right)\implies
S_{\color{brown}{ 8}}=-3\left(\cfrac{1-1679616}{7}\right)
\\ \quad \\
S_{\color{brown}{ 8}}=-3\cdot \cfrac{1-1679616}{7}\to \cfrac{-3\cdot 1-1679616}{7}\)

Answer 38

though.... I don't see anything wrong with the previous anser... the grouped set should be done first.... , unless is not a grouped set

Answer 39

oh I got -229945.57

Answer 40

well... that should read \(\bf S_{\color{brown}{ 8}}=-3\cdot \cfrac{1-1679616}{7}\to \cfrac{-3\cdot (1-1679616)}{7}\)

anyhow.. the subtraction is done first, then the multiplication and THEN the division

Answer 41

oh let meh redo that..

Answer 42

oh got the first option 1. are u sure our error was the pemdas?

Answer 43

actually the last option

Answer 44

yes.... I somehow disagree with it though... the PARENtheses should have done first, and THEN the multiplication

Answer 45

oh okay, me too same

Answer 46

wait I am sorry to confuse you I mean I got option A. Is that what you got too right?

Answer 47

if we use that pemdas arrangement, which I think is wrong, yes

Answer 48

oh okay I'll go with A.

Answer 49

I feel more safe with a..

Answer 50

heheeh

Answer 51

;) lol