Solve the problem involving arithmetic progression

[chwala]

Homework Statement

see attached

Relevant Equations

A.P

I posted this to clarify on the highlighted part- english problem for me.

First less than -200 means what?

Otherwise, the steps to solution are clear... cheers

 

[Hill]

It means, the smallest $n$ for which the sum is less than -200.

 

[pasmith]

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.

 

[pbuk]

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.

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...".

 

[pasmith]

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 $c$.

 

[pbuk]

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.

 

[chwala]

The source of the paper is a past exam international paper. May be confusing to many students across the world.

 

[Gavran]

But here it is stated that the first term (i.e. n = 1) is 5.

This is correct.
In the original post the first term means the initial term.
$a_n=5-3(n-1)$
See https://en.wikipedia.org/wiki/Arithmetic_progression#.

 

[pbuk]

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?

 

[chwala]

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...

 

[pbuk]

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: