Arithmetic Series help (AS Level)

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Homework Help Overview

The discussion revolves around an arithmetic series defined by its first three terms as (12-P), 2P, and (4P-5), where P is a constant. Participants are exploring how to determine the value of P, the sixth term of the series, the sum of the first 15 terms, and how many terms are less than 400.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss setting up equations based on the properties of arithmetic sequences, particularly focusing on the common difference and the general term. There are attempts to derive expressions and clarify the relationships between the terms. Some participants question their calculations and seek confirmation on their reasoning.

Discussion Status

There has been productive engagement, with some participants providing hints and guidance on how to approach the problem. While there is no explicit consensus on the value of P, there is acknowledgment of differing interpretations and calculations. Participants are actively working through the problem and sharing their progress.

Contextual Notes

Some participants note the need to show work for assistance, and there are references to specific parts of the problem that remain unclear, particularly regarding the final part of the question about terms less than 400.

CathyLou
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I'm totally stuck on the following question and so I'd very very grateful if someone could please tell me how to work it out.

The first three terms of an arithmetic series are (12-P), 2P and (4P-5) respectively, where P is a constant.

(a) Find the value of P.

(b) Show that the sixth term of the series is 50.

(c) Find the sum of the first 15 terms of the series.

(d) Find how many terms of the series have a value of less than 400.

Thank you.

Cathy
 
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You have to show some work in order to get help.
 
Present us some of your work. Write down the expression for the general term of an arithmetic sequence, and everything should be more clear. Set up a few equations, and see where they'll bring you.

Edit: late again. :smile:
 
Before I posted I had written the following in response to part a:

an = a1 + (n - 1)d

d = 2p - (12 - p)

d= (4p - 5) - 2p

2p - (12 - p) = (4p - 5) - 2p

4p = (4p - 5) + (12 - p)

Then I got d = 7 but I got confused over the value of p.

Am I working on the right lines?

Thanks for replying by the way! :smile:

Cathy
 
No, p should equal 7.
 
radou said:
No, p should equal 7.

Oh, okay, I get where I went wrong. Thank you.

So, for part b do I just substitute in p to the equation to find d?

Cathy
 
CathyLou said:
Oh, okay, I get where I went wrong. Thank you.

So, for part b do I just substitute in p to the equation to find d?

Cathy

Yes, you do. I.e., d must equal a3 - a2, and a2 - a1, doesn't matter which difference you take.
 
Thanks for your help.

I've now worked out parts a, b and c but I'm still unsure how to do d. Any hints would be really appreciated.

Cathy
 
Basically, you can solve part (d) unformally by trying to plug in different numbers n into an = a1 + (n - 1)*d and see which one is the greatest term which is less than 400.
 
  • #10
radou said:
Basically, you can solve part (d) unformally by trying to plug in different numbers n into an = a1 + (n - 1)*d and see which one is the greatest term which is less than 400.

Okay, thanks very much! :biggrin:

Cathy
 

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