Infinite Geometric Series Help! (1 Viewer)

[Zak Ambrose]

Find the first 3 terms of a Geometric Sequence given that the sum of the first four terms is 65/3 and the sum to infinity is 27.

any help appreciated.

 

[Aerath]

Look at attached answers - I'm pretty sure it's right.

 

[Zak Ambrose]

thank you very much, been struggling over that one for awhile now.
the answer is correct, 9, 6, 4
apparently it could have been 45, -30, 20 aswell [according to textbook]

 

[lyounamu]

thank you very much, been struggling over that one for awhile now.
the answer is correct, 9, 6, 4
apparently it could have been 45, -30, 20 aswell [according to textbook]

That's because r = -2/3 as well (recall: (-2/3)^4 = 16/81)

So if you substitute r = -2/3 as well, you will get a/(5/3) = 27 making a = 45

 

[Aerath]

Aw fuck, I was debating whether or not -2/3 was an answer. My bad, sorry.

 

[Zak Ambrose]

those 2 answer ones always catch me.

thanks!


one more question. i just got caught at the end of this one.

how many terms of the sequence 6, -12, 24, ... are required to give a sum of 1026.


i couldn't get past.
(-2)^n = 512

 

[Aerath]

I ended up getting (-2)ⁿ = -512
Instead of positive 512. Doesn't matter, it still didn't give me an answer.

 

[Zak Ambrose]

oh sorry, i ended up with
(-2)^n = -512
hmm... so that means n has to a an odd number.

perhaps some old fashion trial and error.

-2^3 = -8
-2^5 = -32
-2^7 = -128
-2^9 = -512

so n=9

but there must be a better way than trial and error/

 

[lyounamu]

oh sorry, i ended up with
(-2)^n = -512
hmm... so that means n has to a an odd number.

perhaps some old fashion trial and error.

-2^3 = -8
-2^5 = -32
-2^7 = -128
-2^9 = -512

so n=9

but there must be a better way than trial and error/

Well, (-2)^n = -512

-2^n = -512 (since n = odd number anyway)
2^n = 512
n = ln2(512)
= 9

Sorry, I just woke up so I didn't realise that there was new question. (left my computer open, lol)

 

[Aerath]

Well, (-2)^n = -512

-2^n = -512 (since n = odd number anyway)
2^n = 512
n = ln2(512)
= 9

Just wondering - why is n an odd number?

 

[lyounamu]

Just wondering - why is n an odd number?

n has be to an odd number because if n is an even number, anythiing to the power of postivive must be positive. But in that case, it was negative so n must be an odd number. (except 0)

 

[Aerath]

n has be to an odd number because if n is an even number, anythiing to the power of postivive must be positive. But in that case, it was negative so n must be an odd number. (except 0)

But you're just assuming that n is odd, just for the sake of your answer being right. =\
I'm so lost.

 

[lyounamu]

But you're just assuming that n is odd, just for the sake of your answer being right. =\
I'm so lost.

I am not really assuming because it is the way it is.

(asdasda)^even number (except 0) = positive number where asldjaljd can be anything except 0.

but if you have (-alkdjsaljd)^odd number = negative. From that, I deduced that the number is odd. If examiner was looking for decent working out, I would have explained in the middle why the number is odd not even.

 

[Zak Ambrose]

Well, (-2)^n = -512

-2^n = -512 (since n = odd number anyway)
2^n = 512
n = ln2(512)
= 9

Sorry, I just woke up so I didn't realise that there was new question. (left my computer open, lol)

sorry, what does ln2(512) mean?

 

[lyounamu]

sorry, what does ln2(512) mean?

log2(512)

Don't worry about it if you have not learnt it. It's just 512 in the base of log 2.

 

[Aerath]

I am not really assuming because it is the way it is.

(asdasda)^even number (except 0) = positive number where asldjaljd can be anything except 0.

but if you have (-alkdjsaljd)^odd number = negative. From that, I deduced that the number is odd. If examiner was looking for decent working out, I would have explained in the middle why the number is odd not even.

Yeah, I know what you mean.
My friend gave me a better explanation. "n" has to be odd, because every even number in the series is negative, and is bigger than it's preceding numbers. If the sum of all the equations is positive, therefore, the last number is positive. Since every odd number is positive, n must be odd.

I'm just a little uncomfortable with your explanation, lyounamu, because, although you're right, you're assuming things, to make the answer right (which, it is). Sorry for being a pain.

 

[Zak Ambrose]

i guess ill just count it out until i start the calculus unit or whatever it is.
sorry for the bombardment of questions, had to do geometric sequences and series in the holidays. bastard teacher.

2m - 8, 2m + 4, 5m - 2, are successive terms of G.S. find m.

 

[lyounamu]

i guess ill just count it out until i start the calculus unit or whatever it is.
sorry for the bombardment of questions, had to do geometric sequences and series in the holidays. bastard teacher.

2m - 8, 2m + 4, 5m - 2, are successive terms of G.S. find m.

2m+4/2m-8 = 5m-2/2m+4
(2m+4)^2 = (5m-2)(2m-8)
4m^2 + 16m + 16 = 10m^2 - 44m + 16
6m^2 - 60m =0
m^2 - 10m =0
m(m-10) = 0
so m = 10 or 0

 

[Aerath]

Why can't m = 0?

 

[lyounamu]

Why can't m = 0?

I did put m = 0. I just copied the wrong one from my word document. I forgot to copy m = 0 and added.