having difficulties with Geometric series question

Watch
bigmansouf
Badges: 20
Rep:
?
#1
Report Thread starter 4 years ago
#1
Q:
Name:  qwq.jpg
Views: 114
Size:  60.2 KB
Please note I am having problems with the first part only.
I tried my best to answer it. I have attached it.


The problem I have is with the worked solutions is how did the author come up with
:
 \frac{1}{a}(\frac{r^{n-1}+r^{n-1}+r^{n-2}+r^{n-31}+...+r^{0}}{r^{(n-1)(n-2)(n-3)..3.2.1}})
I thought that  \frac{1}{a}+\frac{1}{ar} + ....+ \frac{1}{ar^{n-1}} = \frac{1}{a}(r^{0}+r^{-1}+r^{-2}+ r^{-3} + .....+ r^{n-1})
therefore r = common ratio =  r^{-1}

and lastly how did the author need up with  \frac{a^{n-1}n(n-1)}{2P_{n}} where  P_{n}  = a^{n}\frac{r^{n(n-1)/2}}{2} as the answer

I thought  P_{n}  = a^{n}\frac{r^{n(n-1)/2}}{2} is wrong.
Shouldn't  P_{n} = a^{n}r^{\frac{n(n-1)}{2}} ?
Please if someone can be kind to explain to me thank you

Edit: Please don't worry about the second part of the question
 \frac{1}{(a)(ar).....(ar^{n-1})} I did this question


the author's solution has been added
Attached files
0
reply
ghostwalker
  • Study Helper
Badges: 17
#2
Report 4 years ago
#2
(Original post by bigmansouf)
The problem I have is with the worked solutions is how did the author come up with:
 \frac{1}{a}(\frac{r^{n-1}+r^{n-1}+r^{n-2}+r^{n-31}+...+r^{0}}{r^{(n-1)(n-2)(n-3)..3.2.1}})
No idea - just looks wrong.

I thought that  \frac{1}{a}+\frac{1}{ar} + ....+ \frac{1}{ar^{n-1}} = \frac{1}{a}(r^{0}+r^{-1}+r^{-2}+ r^{-3})
therefore r = common ratio =  r^{-1}
I assume you meant that to continue, rather than stop at r^{-3}

If so, then agreed.

Though in your subsequent working you should have 1-(1/r) in the denominator, not 1-r.

and lastly how did the author need up with  \frac{a^{n-1}n(n-1)}{2P_{n}} where  P_{n}  = a^{n}\frac{r^{n(n-1)/2}}{2} as the answer

I thought  P_{n}  = a^{n}\frac{r^{n(n-1)/2}}{2} is wrong.
Shouldn't  P_{n} = a^{n}r^{\frac{n(n-1)}{2}} ?
Please if someone can be kind to explain to me thank you
Looks like another error in the book
0
reply
bigmansouf
Badges: 20
Rep:
?
#3
Report Thread starter 4 years ago
#3
(Original post by ghostwalker)
No idea - just looks wrong.



I assume you meant that to continue, rather than stop at r^{-3}

If so, then agreed.

Though in your subsequent working you should have 1-(1/r) in the denominator, not 1-r.



Looks like another error in the book
its the same book i showed you in the other thread

this is the solution it gave Name:  a4.jpg
Views: 105
Size:  70.9 KB
0
reply
ghostwalker
  • Study Helper
Badges: 17
#4
Report 4 years ago
#4
(Original post by bigmansouf)
its the same book i showed you in the other thread
I thought it was the same volume.

I stand by my previous post.
0
reply
bigmansouf
Badges: 20
Rep:
?
#5
Report Thread starter 4 years ago
#5
(Original post by ghostwalker)
I thought it was the same volume.

I stand by my previous post.
Sorry i want to ask are you familiar with AEB questions?
0
reply
ghostwalker
  • Study Helper
Badges: 17
#6
Report 4 years ago
#6
(Original post by bigmansouf)
Sorry i want to ask are you familiar with AEB questions?
Difficult to know, I don't associate any particular questions with AEB - even had to look up what the abbreviation meant.
0
reply
bigmansouf
Badges: 20
Rep:
?
#7
Report Thread starter 4 years ago
#7
(Original post by ghostwalker)
Difficult to know, I don't associate any particular questions with AEB - even had to look up what the abbreviation meant.

AEB - associated examining board

I wanted to ask about questions like this:
The ninth term of an arithmetic progression is 52 and the sum of the first twelve terms is 414. Find the first term and common difference. The rth term of an arithmetic progression (1+4r). Find, in terms of n, the sum of the first n terms of the progression.

The point i wanted to make is the The rth term of an arithmetic progression (1+4r). part. From your opinion do you think that this part is added to distract or confused students.
0
reply
ghostwalker
  • Study Helper
Badges: 17
#8
Report 4 years ago
#8
(Original post by bigmansouf)
AEB - associated examining board

I wanted to ask about questions like this:
The ninth term of an arithmetic progression is 52 and the sum of the first twelve terms is 414. Find the first term and common difference. The rth term of an arithmetic progression (1+4r). Find, in terms of n, the sum of the first n terms of the progression.

The point i wanted to make is the The rth term of an arithmetic progression (1+4r). part. From your opinion do you think that this part is added to distract or confused students.
I would take this to be two different questions, or two parts of a question dealing with two different series.

From the way you've written it, it looks to be one, but that may just be how you've written it.

Can you link/scan/photo the original?
0
reply
DFranklin
Badges: 18
Rep:
?
#9
Report 4 years ago
#9
(Original post by ghostwalker)
I thought it was the same volume.

I stand by my previous post.
To be brutally honest, it doesn't look like the author should be writing books about mathematics!
1
reply
bigmansouf
Badges: 20
Rep:
?
#10
Report Thread starter 4 years ago
#10
Name:  a5.jpg
Views: 120
Size:  136.6 KB
(Original post by ghostwalker)
I would take this to be two different questions, or two parts of a question dealing with two different series.

From the way you've written it, it looks to be one, but that may just be how you've written it.

Can you link/scan/photo the original?
number Q 25 thank you
0
reply
ghostwalker
  • Study Helper
Badges: 17
#11
Report 4 years ago
#11
(Original post by bigmansouf)
number Q 25 thank you
This material is a reworked copy of the original, and, IMO, has lost a bit in transcription. It's not designed to confuse or trick you.

Can't get hold of the original paper, but I would think this question was originally split into two parts, and it certainly refers to two different APs.
0
reply
ghostwalker
  • Study Helper
Badges: 17
#12
Report 4 years ago
#12
(Original post by DFranklin)
To be brutally honest, it doesn't look like the author should be writing books about mathematics!
Agreed. Out of interest I tracked down the publishers. It's a private limited company with two shareholders. No prizes for guessing who the company director is!

Didn't realise vanity publishing extended to the academic sector - perhaps I'm being a bit mean there....
0
reply
bigmansouf
Badges: 20
Rep:
?
#13
Report Thread starter 4 years ago
#13
(Original post by ghostwalker)
Agreed. Out of interest I tracked down the publishers. It's a private limited company with two shareholders. No prizes for guessing who the company director is!

Didn't realise vanity publishing extended to the academic sector - perhaps I'm being a bit mean there....
(Original post by DFranklin)
To be brutally honest, it doesn't look like the author should be writing books about mathematics!
thank you very much
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

What support do you need with your UCAS application?

I need help researching unis (3)
9.68%
I need help researching courses (2)
6.45%
I need help with filling out the application form (3)
9.68%
I need help with my personal statement (14)
45.16%
I need help with understanding how to make my application stand out (6)
19.35%
I need help with something else (let us know in the thread!) (1)
3.23%
I'm feeling confident about my application and don't need any help at the moment (2)
6.45%

Watched Threads

View All