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 October 3rd, 2010, 08:12 AM #1 Newbie   Joined: Oct 2010 Posts: 10 Thanks: 0 Please help this problem is driving me nuts!!! Sarah has an addiction to gum. Each day she goes to her always stocked storage vault and grabs gum to chew. At the beginning of her habit she chewed three pieces and then each day she chews 8 more pieces than she chewed the day before to satisfy her craving. A) How many pieces will she chew on the 793rd day of her habit? B) How many pieces will she chew on the Kth day of her habit? C) How many pieces will she chew over the course of the first 793rd days of her habit? 2. Assume now that sarah at the beginning of her habit chewed M pieces of gum and then each day she chews N more pieces than she chewed the day before. How many pieces will she chew over the course of the first K days of her habit? Explain your formula and how you know it will work for any M, N, and K.
October 3rd, 2010, 08:49 AM   #2
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You have:

$a1= 3$
$a_n= a_1 + (n-1)d , d = 3$

So,$a_n= 8n - 5$

Sum formula:

$S= \frac n 2 (a_1 + a_n) = \frac n 2 ( 3 + 8n - 5) = 4n^2 - n$

Quote:
 A) How many pieces will she chew on the 793rd day of her habit?
$a_{793}= 8(793) - 5 = 6339$

Quote:
 B) How many pieces will she chew on the Kth day of her habit?
$a_k= 8k - 5$

Quote:
 C) How many pieces will she chew over the course of the first 793rd days of her habit?
$S_{793}= 4(793)^2 - 793 = 2,514,603$

Quote:
 2. Assume now that sarah at the beginning of her habit chewed M pieces of gum and then each day she chews N more pieces than she chewed the day before. How many pieces will she chew over the course of the first K days of her habit? Explain your formula and how you know it will work for any M, N, and K.
$a_1= M$

$d= N$

$a_n= M + (n-1)N = Nn + M - N$
So,
$S_k= \frac k 2 ( a_1 + a_k ) = \frac {NK^2} 2 + (M - \frac N 2 )k$

 October 3rd, 2010, 09:22 AM #3 Newbie   Joined: Oct 2010 Posts: 10 Thanks: 0 Re: Please help this problem is driving me nuts!!! Thank you so much!! I do have one more question to ask to clarify the solution you gave me.. In part C of the first question Where did the 4 come from in your equation?
October 3rd, 2010, 09:33 AM   #4
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Quote:
 In part C of the first question Where did the 4 come from in your equation?
From the sum formula I mentioned at the begining:

$S_n= 4n^2 - n$

Just replace n with 793..

 October 7th, 2010, 09:19 AM #5 Newbie   Joined: Oct 2010 Posts: 10 Thanks: 0 Re: Please help this problem is driving me nuts!!! I am still a bit confused, if you don't mind can you explain how you got the sum of the whole problem...step by step so I can understand better. I would really appreciate it. You have been such a help so far!!

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