S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Fri, 24 May 2013 01:06:45 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 10 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 01:06:36 UTC
 Member

Joined: Thu, 7 Jul 2011 18:07:39 UTC
Posts: 11
I need some help here! We've been given the formula for Arithmetic and Geometric Progressions but the problems below, I cannot apply the formula. Its kinda tricky. Would you help me? These are sample questions for our long test. I need these so I can reviewT_T

1 Find an arithmetic progression if the sum of its first four terms is equal to 26 and the product of the same terms equals 880.

2. An arithmetic progression consists 20 terms. The sum of the terms occupying even places equals 259 while that of the terms occupying odd places equals 220. Find the two medium terms of the progression.

3 Find the four numbers forming a geometric progression in which the sum of the extremes is 27 and the product of the means is 72.

THANK YOU VERY MUCH.

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 01:53:32 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
bummielove wrote:
I need some help here! We've been given the formula for Arithmetic and Geometric Progressions but the problems below, I cannot apply the formula. Its kinda tricky. Would you help me? These are sample questions for our long test. I need these so I can reviewT_T

1 Find an arithmetic progression if the sum of its first four terms is equal to 26 and the product of the same terms equals 880.

2. An arithmetic progression consists 20 terms. The sum of the terms occupying even places equals 259 while that of the terms occupying odd places equals 220. Find the two medium terms of the progression.

3 Find the four numbers forming a geometric progression in which the sum of the extremes is 27 and the product of the means is 72.

THANK YOU VERY MUCH.

Remember, an arithmetic progression is where d is the common difference. So if we sum up all of the first FOUR terms say, that's This means , now divide both sides by 2 and you get .

So we make the reasonable guess that , which by gives us . Now we check, does this indeed work? Well, we get: , so we're good.

(If this had not worked, we'd next try which would give , but that one doesn't work. Basically try the nice numbers until you get one that works.

2. This time I'll start the first term calling it and you'll see why, then the even terms are:

which is impossible because the left side is even and the right side is not. Even if you assume the first term is the zeroth term, you'll end up with an even thing on the left because it will be

3. Again, four numbers, label the common ratio as r, and then we get: The sum of the extremes is , but I don't understand what you mean by "means" which mean are you talking about? Which numbers are you averaging to get these means?

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 03:27:53 UTC
 Member

Joined: Thu, 7 Jul 2011 18:07:39 UTC
Posts: 11

3. Again, four numbers, label the common ratio as r, and then we get: The sum of the extremes is , but I don't understand what you mean by "means" which mean are you talking about? Which numbers are you averaging to get these means?

Maybe the means are the middle two terms and the extremes are the outer two terms (?). I have no idea. =))

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 03:28:53 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
bummielove wrote:

3. Again, four numbers, label the common ratio as r, and then we get: The sum of the extremes is , but I don't understand what you mean by "means" which mean are you talking about? Which numbers are you averaging to get these means?

Maybe the means are the middle two terms and the extremes are the outer two terms (?). I have no idea. =))

The means are definitely the first and last, but I'm fairly confident means signifies what I think it does, which is something techinical.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 03:39:08 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Hmm, okay so possibly the numbers involved are not integers, but then that's a really wacky question to ask for someone at your level. I'll try and think on it more to make sure there's really not much you can do.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 03:39:46 UTC
 Member

Joined: Thu, 7 Jul 2011 18:07:39 UTC
Posts: 11
Hmm, okay so possibly the numbers involved are not integers, but then that's a really wacky question to ask for someone at your level. I'll try and think on it more to make sure there's really not much you can do.

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 03:45:00 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Oh, Okay, I got it. I was silly and forgot a bunch of terms, sorry about that.

Here we go.

You're supposed to subtract.

the sum of the ten evens is and the sum of the first ten evens is:

subtract and you get:

so

From this it is easy to get the two middle terms, you can just use to solve for then get the two middle terms directly.

(note: I get the number of times I add by using the fact that the sum of the first n odd numbers is and the sum of the first n even numbers (starting at 0) is )

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 17:29:27 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, bummielove!

Quote:
2. An arithmetic progression consists 20 terms.
The sum of the terms occupying even places equals 259,
while that of the terms occupying odd places equals 220.
Find the two medium ? terms of the progression.
I assume you mean the two middle terms.

The sequence of "even" terms has first term , common difference , and terms.
. . Its sum is: . .[1]

The sequence of "odd" terms has first term , common difference , and terms.
. . Its sum is: . .[2]

Subtract [1] - [2]: .

Substitute into [2]: .

Therefore: .

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Fri, 26 Aug 2011 19:03:46 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
Soroban wrote:
Hello, bummielove!

Quote:
2. An arithmetic progression consists 20 terms.
The sum of the terms occupying even places equals 259,
while that of the terms occupying odd places equals 220.
Find the two medium ? terms of the progression.
I assume you mean the two middle terms.

The sequence of "even" terms has first term , common difference , and terms.
. . Its sum is: . .[1]

The sequence of "odd" terms has first term , common difference , and terms.
. . Its sum is: . .[2]

Subtract [1] - [2]: .

Substitute into [2]: .

Therefore: .

Um, if those are consecutive terms, shouldn't they vary by 3.9? 25.0-22.0=3.0. . .

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Post subject: Re: Arithmetic and Geometric ProgressionsPosted: Sat, 27 Aug 2011 04:29:47 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
A silly typo! . . . Struck "0" instead of "9".

It should have been:

. . Therefore: .

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 10 posts ]

 All times are UTC [ DST ]

Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous