What is the sum of the geometric sequence –4, 24, –144, ... if there are 6 terms? How do I do this?

Question

meehan98 · Answer

Ok, the equation looks like this:
$$S _{n}=a _{1} \frac{ 1-r ^{n} }{ 1-r }$$

anonymous · Answer

what's S, A, R, and N?

meehan98 · Answer

S= the sum
n=the term that you choose, so for this example it would be 6
$$a _{1}$$= the first term

anonymous · Answer

So exactly how would you set it up? thats all I need to know, can you show me an example?

meehan98 · Answer

Let's break it down a little bit, so it's not so much to take in. We just fill in what we know so: 
$$S _{6}= -4   \frac{ 1-(-6)^{6} }{ 1-(-6)}$$

meehan98 · Answer

I forgot to tell you that we get "r" by 24/-4=-6 because that's our ratio.

drigobri · Answer

This equation does not work @Meehan98
If you try to do for the second term (S2), will hit as the number 20, which is not consistent with the case

anonymous · Answer

Just find the pattern In this case its multiplying by -6

anonymous · Answer

Sohal i'm in trigonometry, i'm not just doing x-6 lol

anonymous · Answer

so the answer would be... 864,-5184,31104 would be the next numbers

anonymous · Answer

Lol but all the information is informant of you -_- and the way you get the answer doesn't matter as long as you don't cheat,show work,and get the right answer

anonymous · Answer

do you deny that I got the right answer?

anonymous · Answer

I found the answer deductivly

anonymous · Answer

Ps I never actually got the answer But I did give you the next numbers of the sequence

meehan98 · Answer

hmm..this doesn't make sense then. I've been doing these problems all day without an issue..

anonymous · Answer

ok do it your way ill do it my way -_- honestly ever herd of doing it in different methods forget it

meehan98 · Answer

I know; because the formula that I have up there is the Sum Formula so it wouldn't make sense to fit the second term in there. The formula for the terms is:$$a _{n}=a _{1} r ^{n-1}$$

drigobri · Answer

If you get the second number and divide by the first, will result 6. If you made the third number and divide by the first, will result in 36, which is 6 ^ 2, we can quickly realize the equation, that is:
$$n = 4 x (-6^{(n-1)})$$
where:
n = number wish to find

So,
$$n1= -4 . (-6^{1-1}) = -4 . (1) = -4$$$$n2= -4 . (-6^{2-1}) = -4 . (-6) = 24$$$$n3= -4 . (-6^{3-1}) = -4 . (36) = -144$$$$n6= -4 . (-6^{6-1}) = -4 . (-46656) = +186624$$

drigobri · Answer

we can quickly realize the equation, that is:
n=-4x(−6(n−1))***** << I forgot -4 there