Question

What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms

Answer 1

@kirbykirby

Answer 2

Eighty-Nineeeeeee

Answer 3

−959,781

29,637

26,661

959,780

Answer 4

anybody know the actual equation to find these?

Answer 5

\[\Large \sum_{k=1}^nar^{k-1}=a\left( \frac{1-r^n}{1-r}\right) \] where \(r\) is the common ratio, which you can find by dividing the 2nd term with the 1st, or the 3rd term with the 2nd, etc.

Answer 6

ohh yeah my calculator has the equation input for that, what does n stand for? is that the first term or the one we are trying to find?

Answer 7

Well notice that \[\Large \sum_{k=1}^nar^{k-1}=a+ar+ar^2+\ldots+ar^{n-1}\\ \Large \Large \sum_{k=1}^{8}ar^{k-1}=-4+24-144+...+ar^{8-1}\]

Answer 8

https://www.khanacademy.org/math/precalculus/seq_induction/geometric-sequence-series/v/geometric-series

Answer 9

ok so are n is the term we are trying to find, now why does our variable = 1?

Answer 10

well it starts at k=1, and goes until k=8, for 8 terms. You should see though from the way I wrote the sum:
\(a = -4 \\
ar = 24 \)
You can deduce \(r\) and then use the formula in my first post

Answer 11

ooh ok gotcha, i was wandering because when i put it into my calc it has tobe right

Answer 12

hmm normaly when the equation is already laid out it comes up right, but im getting large numbers, what would the expression be

Answer 13

because i enter it in like this.. Expression,variable,low,high
all are correct but the exp

Answer 14

\[ \Large \sum_{k=1}^8-4(-6)^{k-1}=(-4)\left(\frac{1-(-6)^8}{1-(-6)}\right)\]

Answer 15

ok i got the -4 in the exp correct but where did the 6 come from

Answer 16

That's the \(r\), and its -6

a = -4
ar = 24

Divide the 2nd equation by the 1st:
\[\frac{ar}{a}=\frac{24}{-4}\implies r = -6 \]

Answer 17

oh thats right r = ratio

Answer 18

yup !

Answer 19

i think my calculator isnt reading it right i have never had it do this but its giving me \[\frac{ 239945 }{ 419904 }\]

Answer 20

try like:(-4)*((1-(-6)^8)/(1+6))

Answer 21

If you are typing in the inputs for some "geometric series" function on your calculator.. Well to be honest I am not sure what your calculator is doing, or how the inputs must be put in. I never used a graphing calculator, I only ever had a simple scientific calculator. I just rely on the formulas such as the one abov

Answer 22

im using the TI nSpire cx cas and all i do is go to the "Glossary" and find that backwards e thing and it says to input it as such
Exp.Var,Low,High

Answer 23

normally i get problems that already have it written out and i just input the values to solve

Answer 24

ok using ur formula i got D

Answer 25

Hm. Well I think this is a case of "blindly" using the calculator without knowing exactly what it's doing :) Um, if you have your calculator's instructions, you should be able to see what he calculator is doing in that function, and type in the appropriate inputs accordingly.

Answer 26

Again, I don't have this calculator so I can't help too much in regards to using it :(

Answer 27

it has it written out in its description in the glossary. its almost like its not reading it for example normally when i come across these problems it looks like this

\[\sum_{i=7}^{21}\](4-2)^i-1

now that example probably doesnt equal anything or even work but then i have four choices, i enter it into my calc as the example is written and it gives me the answer, i have never seen it do this before

Answer 28

almost like we arent writing it like it would read it.. im baffled,, but i wish i could figure out whats wrong because i have 3 more of these problems that i need to do and i dont want to keep asking help on the same types of problems

Answer 29

Hm give me a sec I will try and search for the instructions online for your calculator. (I do have to do you are lucky you can use it for your problems haha. But it's always good to know how to go back to basics :) )

Answer 30

Ok so it looks like this? https://epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=109208

Answer 31

yeah but u know whats funny i did not know you could fill out the values like that ive always done it like \[\Sigma(Expression,Variable,Low,High)\]

Answer 32

u showed me sumthing new about my own calc lol

Answer 33

oh interesting haha

Answer 34

it came up with that answer first try!

Answer 35

when i did it like that page did it

Answer 36

did not even know sigma was calc. im retaking alg 2

Answer 37

yay :)

Answer 38

but now how again did you determine six? in the expression?

Answer 39

r is the common ratio, to do that quickly:
Divide the 2nd term by the 1st

Answer 40

so 24/(-4) = -6

Answer 41

now deos dividing the second by the first always work?

Answer 42

yes always :)

Answer 43

ok im gonna work another one out and then tag u to make sure i did it correctly

Answer 44

coolies ;)