Help Needed: Geometric Progression & Arithmetic Sums

In summary, the conversation discusses the difficulties the speaker is having with geometric progressions and arithmetic series. They share their work and ask for help with two particular problems. One mistake that was caught was forgetting to properly square a fraction in one of the problems.
  • #1
mr_coffee
1,629
1
Hello everyone I'm studying for my next exam and I screwed up on the geometric progressions and arthm and they are the easiest of them all but I don't know what I'm doing wrong.

The first problem on the exam said:
Suppose that an arithmetic series has 202 terms. If the first term is 4PI and the last term is 60-4PI, what is the sum of the sries?

I came out with 6060, my work is posted below ( i think i got it right this time)

Now for the real problem, Write down the formula of the following sum:
You can see my work at the bottom but as you can see, it doesn't check out with adding up the terms by hand and usuing my formula. I'm really not sure what I did wrong here. ANy help would be great:
http://suprfile.com/src/1/4apu96r/lastscan.jpg



Also another one is #3. It says Write down the formula of the sum, simplify your answer, and now check when n = 1, n = 2, n = 3.

Again the formula and adding the terms up by hand arn't working out.
http://suprfile.com/src/1/4apvbsk/lastscan.jpg
 
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  • #2
Your images aren't working.

You got the first question right though
 
  • #3
Thanks for the responce, how about now?
http://suprfile.com/src/1/4apu96r/lastscan.jpg and

http://suprfile.com/src/1/4apvbsk/lastscan.jpg
 
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  • #4
Just a quick glance... one error that seemed to pop out at me is,

Check (3/2)^2. I think it was just a careless mistake; you didn't put parentheses around the 3/2 and ended up forgetting to square the denominator as well.
 

What is a geometric progression?

A geometric progression is a sequence of numbers where each term is found by multiplying the previous term by a constant number. For example, in the sequence 2, 4, 8, 16, the constant number is 2 and each term is found by multiplying the previous term by 2.

What is the formula for finding the sum of a geometric progression?

The formula for finding the sum of a geometric progression is Sn = a * (1 - r^n) / (1 - r), where Sn is the sum of the first n terms, a is the first term, and r is the common ratio.

How is a geometric progression different from an arithmetic progression?

A geometric progression is a sequence of numbers where each term is found by multiplying the previous term by a constant number, while an arithmetic progression is a sequence of numbers where each term is found by adding a constant number to the previous term.

What is an arithmetic sum?

An arithmetic sum is the sum of a finite number of terms in an arithmetic progression. It is found by multiplying the average of the first and last term by the number of terms in the sequence.

How can geometric progressions and arithmetic sums be applied in real life?

Geometric progressions and arithmetic sums are often used in financial calculations, such as compound interest and loan payments. They can also be used in population growth and other natural phenomena that follow a pattern of exponential or linear growth.

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