## I need help developing an equation

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
cloyd
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Joined: Thu Dec 06, 2012 10:00 pm
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### I need help developing an equation

I am trying to write an equation but can't seem to remember far enough back in school to figure out how to do it. The example I will give below is simplified and not real world in terms of actual numbers or products. That being said, it should outline my need in order to come up with a formula that could be applied to any number considering the same scenario. Hopefully this is clear.

Let's say an apple costs \$2 for one. I want to buy 100 apples, but they have to be purchased 10 at a time and every time I purchase 10, the price of one apple increases by \$1.50. I want to be able to calculate my total cost for all 100 apples.
If you work this out manually: 2*10 + (2+1.5)*10 + (3.5+1.5)*10 + (5+1.5)*10 + (6.5+1.5)*10 + (8+1.5)*10 + (9.5+1.5)*10 + (11+1.5)*10 + (12.5+1.5)*10 + (14*10)= \$875

I just don't know how to represent all of that into a formula

I would like to be able to substitute any value for "starting cost", "increase in cost", "number to be purchased at one time", and "total number to be purchased" and still calculate the total cost.

Thanks in advance for the help!

buddy
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### Re: I need help developing an equation

Would maybe an arith. series work?
They show it here: http://www.purplemath.com/modules/series4.htm
Your common diff. would be d=1.5

strumbore
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### Re: I need help developing an equation

This is called an "arithmetic series".

Each term in an arithmetic series ALWAYS has a difference of "d" between each term. Subtract any term in this sequence by the one that preceded it and the answer is always d=(I'll let you figure this one out).

If you want to calculate the actual cost of 100 apples, you need to find the sum of the first 10 terms (as each term represents the price of 10 apples in sequence). you can find this easily by plugging the first and last term into a simple equation:

For a FINITE arithmetic sequence,

Sn = (n/2)(a1 + an)

a1=first term, an=last term, n=the total number of terms being added.

Plug these figures in and what do you get?

now, to create *an equation*

The nth term of an arithmetic sequence can be found using a couple of general formulas, but here's the best one you should use (I recommend you look into this)

The nth term of an arithmetic sequence has the form an = dn + c

where c = a1 - d

You take it from there.
Last edited by strumbore on Sat Jan 12, 2013 9:38 am, edited 1 time in total.

jg.allinsymbols
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Joined: Sat Dec 29, 2012 2:42 am
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### Re: I need help developing an equation

cloyd explains this:
Let's say an apple costs \$2 for one. I want to buy 100 apples, but they have to be purchased 10 at a time and every time I purchase 10, the price of one apple increases by \$1.50. I want to be able to calculate my total cost for all 100 apples.
If you work this out manually: 2*10 + (2+1.5)*10 + (3.5+1.5)*10 + (5+1.5)*10 + (6.5+1.5)*10 + (8+1.5)*10 + (9.5+1.5)*10 + (11+1.5)*10 + (12.5+1.5)*10 + (14*10)= \$875
If you are buying in groups of 10, then your first term is not applied. The actual first term will be (2+1.5)*10.

strumbore
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Joined: Fri Jan 11, 2013 12:01 am
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### Re: I need help developing an equation

I guess OP isn't coming back, so the answers are

an= 5(3n-1)

and

Sn=(10/2)[(10)+(145)]= \$775.