Solving Arithmetic and Series Problems in IB Math Methods

In summary, the first question is asking for all possible values of the first term and the second question is asking for the sum of the series as a function of n.
  • #1
Astronomer107
31
0
I've been working on these problems for a long time trying to prove to myself that I'm not stupid (though I am convinced I am because I don't feel like "IB material" at the moment), but this will be impossible since I have other things to do. So, my two questions are these:

1. An arithmetic sequence has a common difference of 2 and a sum of 120. The first term is numerically equal to the number of terms. FInd all possible values of hte first.

I know that the answer is 8 because it is a multiple choice question and through elimination, the others aren't possible, but I don't understand how to prove this mathematically.

2. Determine Sn of the series 4 + 10 + 16 + 22+...+ (6n - 2).

I tried to solve this one, but when I did, the n's canceled out, making it "all real numbers" and since (6n - 2) is the last term, the series isn't infinite.

PLEASE HELP ME! Thanks!
 
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  • #2
1) The series is: [sum] [ x + 2*y] from y = 0 to x-1

To solve an arithmetic series it is 1/2 times the size of the series times the quantity of the first term plus the second

Sn = (1/2) * n * ( a1 + a2 )

the first term you know is the number of terms in the series and the last term is equal to n+2*(n-1) based on the equation.

So..

Sn = (1/2) * n * ( n + [ n + 2*(n-1) ] )

Then you solve Sn = 120

And you get n = 8 and -7.5

2) I'm unsure what your asking

the series is
[sum] 6x-2 from x=1 to ?

your saying the series isn't infinite, so what is it?

if the series goes from x=1 to infinity then the series diverges
 
  • #3
Originally posted by dduardo


Then you solve Sn = 120

And you get n = 8 and -7.5

2) I'm unsure what your asking

the series is
[sum] 6x-2 from x=1 to ?

your saying the series isn't infinite, so what is it?

if the series goes from x=1 to infinity then the series diverges

Thanks for the help on the first question. I was assuming the series was finite because (6x - 2) is the last term in the series. Another question: I don't understand how -7.5 can be relevant because it says that n is equal to the number of terms, but there can't be -7.5 terms... can there?
 
  • #4
I think that what the question for is the sum as a function of n.

Sn = F(n)

What you would do is write out the summation, and then use the rules that you know to reduce it into a formula.

For example:

[sum]c from i=0 to n = cn (c is a constant
[sum]i from i=0 to n = 1/2(i+1)*i
 
  • #5
Astronomer107: -7.5 can occur in a quasi-hyperdimesion manifold, that is forumalated by using the...

No, you are right, -7.5 isn't an answer. (Only in my imagination)

Also, what are the choices for question 2.

Is there an answer: n*(3*n+1)
 

1. What is the difference between IB Math Methods SL and HL?

IB Math Methods SL and HL are both levels of the International Baccalaureate Mathematics curriculum. SL stands for Standard Level and HL stands for Higher Level. The main difference between the two is the depth and complexity of topics covered. HL covers more advanced topics and requires a deeper understanding of mathematical concepts.

2. How many topics are covered in the IB Math Methods curriculum?

There are six main topics covered in the IB Math Methods curriculum: Algebra, Functions and Equations, Circular Functions and Trigonometry, Vectors, Statistics and Probability, and Calculus. Each topic has subtopics that are also covered in the curriculum.

3. Are calculators allowed in the IB Math Methods exams?

Yes, calculators are allowed in IB Math Methods exams. However, there are restrictions on the type of calculator that can be used. Students are only allowed to use a simple scientific calculator that does not have any built-in formulas, graphs, or programming capabilities.

4. What is the internal assessment component of IB Math Methods?

The internal assessment is a project that accounts for 20% of the final grade in IB Math Methods. It is an independent project where students choose a topic of interest related to the course and conduct their own investigation using mathematical methods. The project is graded by the teacher and moderated by the IB.

5. Are there any recommended study resources for IB Math Methods?

Yes, there are several recommended study resources for IB Math Methods. The official IB Math Methods textbook, past papers, and study guides are all helpful resources. There are also online resources such as Khan Academy and IB Math Academy that offer additional practice problems and explanations.

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