Solve the problem involving arithmetic progression

AI Thread Summary
The discussion revolves around clarifying the interpretation of an arithmetic progression problem, specifically regarding the definition of the first term and the number of terms. Participants highlight confusion over whether the first term is defined as n=0 or n=1, with some arguing that the wording of the problem is ambiguous. The source of the problem is identified as a past international exam paper, which may have contributed to the confusion among students. A comparison is made with a better-worded question from a subsequent exam paper, suggesting improvements in clarity. Overall, the conversation emphasizes the importance of precise language in mathematical problem statements.
chwala
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Homework Statement
see attached
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A.P
I posted this to clarify on the highlighted part- english problem for me.

First less than -200 means what?

1728785903791.png


Otherwise, the steps to solution are clear... cheers
 
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It means, the smallest ##n## for which the sum is less than -200.
 
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Hill said:
It means, the smallest ##n## for which the sum is less than -200.

The "number of terms" will be n + 1 rather than n if you start from n = 0, as would be usual.
 
pasmith said:
The "number of terms" will be n + 1 rather than n if you start from n = 0, as would be usual.
But here it is stated that the first term (i.e. n = 1) is 5.
chwala said:
I posted this to clarify on the highlighted part- english problem for me.
The problem is with their English, not yours - they talk about "the number of terms" and they talk about "##n##" but they do not link the two. It should read "Find the number of terms ##n## such that..." or "Find ## n ## such that...".
 
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pbuk said:
But here it is stated that the first term (i.e. n = 1) is 5.

I don't agree.

It is natural to express a term of an arithmetic progression as a_n = c + dn with a_0 = c and not as a_n = c + d(n-1) with a_1 = c. In either case, the first term of the sequence is c.
 
pasmith said:
I don't agree.

I think we are splitting hairs about just how badly worded a badly worded question is. What did they really mean by "the first term is 5"? Does this imply that the first term is ## t_1 = 5 ##? If they had intended this to mean ## t_0 = 5 ## then would they have said "the zero'th term"?

Who knows, they don't even tell you that ## n ## is the number of terms so whether this starts at 0 or 1 is secondary.
 
The source of the paper is a past exam international paper. May be confusing to many students across the world.
 
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chwala said:
The source of the paper is a past exam international paper. May be confusing to many students across the world.
Indeed. Can you provide a link, or failing that state the exam board?
 
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chwala said:
The source of the paper is a past exam international paper. May be confusing to many students across the world.
Sorry, i just checked it is from the specimen paper of 2020 - code 0606/01. Most probably, this was corrected in subsequent papers i think...
 
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chwala said:
Sorry, i just checked it is from the specimen paper of 2020 - code 0606/01. Most probably, this was corrected in subsequent papers i think...
Ah, I see. Here is a link: https://www.cambridgeinternational....gcse-mathematics-additional-0606/past-papers/

In the June 2022 paper 1 there was a similar question which was indeed better worded:

7 (a) The first three terms of an arithmetic progression are ## \operatorname{lg} 3, 3 \operatorname{lg} 3, 5 \operatorname{lg} 3 ##. Given that the sum to ## n ## terms of this progression can be written as ## 256 \operatorname{lg} 81 ##, find the value of ## n ##. [5]​

Note also that in this syllabus (as I believe is the case for all GCSE and IGCSE syllabi), the convention is that the first term of a series is ## a_1 ##. This is also implied in the "Mathematical Formulae" section in the front of the paper:
1728988502560.png
 
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