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: 50.5(111) = 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 50.5(1) = $4.50, not $5 as it wants. So, since "first" usually means n=1, you have to have 50.5(11) = $5
The 'simple explanation' for this problem would be to list the prices: 1st is 50.5(11) = 5 2nd is 50.5(21) = 4.5 3rd is 50.5(31) = 4 4th is 50.5(41) = 3.5 5th is 50.5(51) = 3 6th is 50.5(61) = 2.5 7th is 50.5(71) = 2 8th is 50.5(81) = 1.5 9th is 50.5(91) = 1 10th is 50.5(101) = 0.5 11th is 50.5(111) = 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 a_{n} = a_{n1}  0.5
or
a_{n} = 5  0.5 * (n1)

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? 