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 Expression for sequential decrease

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T O P I C    R E V I E W
corchos68 Posted - 10/10/2012 : 14:59:19
A vendor at the fair sells an item for $5. Every item after that is less 0.50 cents. How many items must you buy before you get a free one? First one is $5, 2nd is $4.50, 3rd is $4 and so on until the eleventh item is free.
Is there a way to write this as an algebra expression?
5   L A T E S T    R E P L I E S    (Newest First)
the_hill1962 Posted - 11/26/2012 : 13:02:33
Looking at the title for this topic, the explanations are great.
However, since this is in the "basic math" section, here is an simple explanation:
5-0.5(11-1) = 0

A lot of students get confused as to why "1" is subtracted.
The easy way is to just refer to the original problem where it states "the FIRST one is $5"
Note that 5-0.5(1) = $4.50, not $5 as it wants.
So, since "first" usually means n=1, you have to have 5-0.5(1-1) = $5

The 'simple explanation' for this problem would be to list the prices:
1st is 5-0.5(1-1) = 5
2nd is 5-0.5(2-1) = 4.5
3rd is 5-0.5(3-1) = 4
4th is 5-0.5(4-1) = 3.5
5th is 5-0.5(5-1) = 3
6th is 5-0.5(6-1) = 2.5
7th is 5-0.5(7-1) = 2
8th is 5-0.5(8-1) = 1.5
9th is 5-0.5(9-1) = 1
10th is 5-0.5(10-1) = 0.5
11th is 5-0.5(11-1) = 0
Subhotosh Khan Posted - 11/20/2012 : 10:44:12
quote:
Originally posted by corchos68

A vendor at the fair sells an item for $5. Every item after that is less 0.50 cents. How many items must you buy before you get a free one? First one is $5, 2nd is $4.50, 3rd is $4 and so on until the eleventh item is free.
Is there a way to write this as an algebra expression?




a = 5
an = an-1 - 0.5

or

an = 5 - 0.5 * (n-1)
royhaas Posted - 10/12/2012 : 08:05:00
The clue lies in the fact that the difference between successive terms is constant. Perhaps conducting an Internet search for "arithmetic progression" or "arithmetic series" will help.
corchos68 Posted - 10/11/2012 : 14:30:57
quote:
Originally posted by royhaas

Do you know what an arithmetic progression is?



I don't. The homework asked if I could think of a different way to express my work - and I could not though I imagined there exists a simple or at least more elegant way than what I did.
royhaas Posted - 10/11/2012 : 08:22:20
Do you know what an arithmetic progression is?

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