anonymous
  • anonymous
Four friends agree to save money for a graduation road trip. They decide that each of them will put $0.25 in the fund on the first day of May, $0.50 on the second day, $0.75 on the third day, and so on. At the end of May, there will be $_____ in their fund. (Hint: There are 31 days in May.)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
how much do you know about summations?
anonymous
  • anonymous
Arithmetic series.
anonymous
  • anonymous
If im correct i think the equation should be : Sn=(n/2)(a1+n) multiply the sum by four

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More answers

anonymous
  • anonymous
would that equation be right?
anonymous
  • anonymous
the easiest way (at least for me) is to represent it as \[4 \sum_{n=1}^{31} \frac{ n }{ 4 }\]
anonymous
  • anonymous
which simplifies to \[\sum_{n=1}^{31} n\]
anonymous
  • anonymous
wait that seems complicated -.-
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
|dw:1378182300065:dw|
anonymous
  • anonymous
0.0 okay so then it would be 496.. multiply that by 4 because 4 of them are contributing, then it equals to 1875.50 right
mathstudent55
  • mathstudent55
No. Each is contributing $0.25 on the first day. All 4 friends contribute $1 more each day. The sum 1 + 2 + ... + 31 already takes into account all 4 friends. The answer is $496.
mathstudent55
  • mathstudent55
|dw:1378182591632:dw|
anonymous
  • anonymous
wouldnt each mean individually? so then 496 would be for one person. the equation is only counting one person, multiplying the sum 496 by four would complete the meaning "each of them will put in "
anonymous
  • anonymous
the equation is for all 4 together
anonymous
  • anonymous
oh okay then....
mathstudent55
  • mathstudent55
No. Remember each person starts with a $0.25 contribution on the first day. For each individual, the sum is: $0.25 + $0.50 + $0.75 + ...
anonymous
  • anonymous
okay...
mathstudent55
  • mathstudent55
You can factor the 0.25 out of the sum: $0.25 + $0.50 + $0.75 + ... = 0.25(1 + 2 + 3 + ...) But this is still per individual.
mathstudent55
  • mathstudent55
Now you multiply the factored sum by 4 since there are 4 friends: 4 * 0.25(1 + 2 + 3 + ...) = 1 * (1 + 2 + 3 + ...) = 1 + 2 + 3 + ...
mathstudent55
  • mathstudent55
It's a coincidence that the number of friends and the amount is $0.25 = 1/4 which when multiplied give you 1.
anonymous
  • anonymous
\[S _{n}=(\frac{ n }{ 2 })(a _{1}+n)\]) \[S _{31}=(\frac{ 31 }{ 2 })(.025+30)\]) =15.5(3.25) =$468.875 Four people contributing: 468.875(4)= 1875.50 Their total funds at the end of may would be $1875.50 okay i understand.. the above was just what i did
mathstudent55
  • mathstudent55
Sum of first n integers: \(S_n = \dfrac{n(n + 1)}{2} \)
mathstudent55
  • mathstudent55
I know you closed this question, but since you wrote your last response, I now understand what you were trying to do. The sum of the first n terms of an arithmetic series is: \(S_n = \dfrac{n}{2}(a_1 + a_n) \) In order to find the sum, you need the first and last terms of the series, \(a_1\) and \(a_n\), and the number of terms, n. To find the sum of the contributions of one single friend, you know the first term is 0.25. What did one friend contribute on the 31st day? For that, we use the formula to find the nth term of an arithmetic sequence: \(a_n = a_1 + (n - 1)d \), where d is the common difference. Now we can find \(a_{31} \): \(a_{31} = 0.25 + (31 - 1)(0.25) \) \(a_{31} = 0.25 + 30(0.25) \) \(a_{31} = 0.25 + 7.50 \) \(a_{31} = 7.75 \) Now with \(a_1 = 0.25\) and \(a_{31} = 7.75\), we can use the formula for the sum of an arithmetic series: \(S_n = \dfrac{n}{2}(a_1 + a_n) \) \(S_{31} = \dfrac{31}{2}(0.25 + 7.75) \) \(S_{31} = 15.5(8) \) \(S_{31} = 124 \) Each friend contributed $124. All 4 friends contributesd \(4 \times $124 = $496\).

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