anonymous
  • anonymous
ARITHMETIC SERIES WORD PROBLEM!! PLEASE HELP!! \'O'/
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Sally just started working at this new daycare center that opened. The first day 100 children came. For each following day for a month, 30 more start coming. How many children come on the 7th day?
anonymous
  • anonymous
Okay, so I know I use the formula Sn = n/2[2a + (n-1)d ]
anonymous
  • anonymous
I'm just a little stuck with what to plug in where...

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anonymous
  • anonymous
Sn = 7/2 is all i know so far...
anonymous
  • anonymous
how do i find the common difference?
mathslover
  • mathslover
What is n here?
anonymous
  • anonymous
100?
mathslover
  • mathslover
No, can you tell me what does n symbolizes?
mathslover
  • mathslover
I mean , what does n stand for?
anonymous
  • anonymous
the first term in the series?
anonymous
  • anonymous
wait no! hold on
mathslover
  • mathslover
No! @helpmepassalgebra2 the first term in the series = \(\large a\) the total terms = \(\large n \) the last term = \(\large a_n\)
anonymous
  • anonymous
its the position number of a given term
mathslover
  • mathslover
And the common difference = d.
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
so there's 7 terms?
mathslover
  • mathslover
Here I can write the series as : 100, 130, ... , \(a_7\) as, here , n = 7 so I wrote the last term as \(a_n = a_7\) ... Understanding ?
anonymous
  • anonymous
yes
mathslover
  • mathslover
So now, what is the common difference , @helpmepassalgebra2 ?
anonymous
  • anonymous
uh minus 30?
anonymous
  • anonymous
i mean plus
mathslover
  • mathslover
Good.
anonymous
  • anonymous
okay so that means...Sn = 7/2[2a + (7-1)30 ]
anonymous
  • anonymous
but whats 2a again?
mathslover
  • mathslover
Now, see we have : n =7 a = 100 d = 30 since : \(\large S_n = \cfrac{n}{2} (2a + (n-1)d) \) \(\large S_n = \cfrac{7}{2} (200 + 180) \) \(\large S_n = \cfrac{7}{2} * 380 \) \(\large S_n = 1330 \)
anonymous
  • anonymous
is it 100? the first term?
mathslover
  • mathslover
2a = 2*a as : a = 100 so 2a = 200
anonymous
  • anonymous
wow thanks for writing it out like that so i can see how to do it! :D
anonymous
  • anonymous
thank you so much!!
mathslover
  • mathslover
Though, the question is not yet complete my dear friend.
anonymous
  • anonymous
oh really?? O.o what else do we have to do then?
mathslover
  • mathslover
We have to calculate \(a_7\) And as per the formula : \(\large S_n = \cfrac{n}{2} (2a + (n-1)d) \) \(\large S_n = \cfrac{n}{2} ( a +\{ a+ (n-1)d \} )\) \(\large S_n = \cfrac{n}{2} (a + a_n ) \) \(...\) \(\large \textbf{as :} \space a + (n-1)d = a_n \) \(1330 = \cfrac{7}{2} ( 100 + a_n) \)
mathslover
  • mathslover
Note, we have to calculate the 7th term , and what we found was "the sum of all terms (S_n) "
anonymous
  • anonymous
okay
mathslover
  • mathslover
Can you calculate it , by understanding the above mentioned method?
anonymous
  • anonymous
what does an respresent again?
anonymous
  • anonymous
sorry idk how to write that like u did.. its a with a small n beside it or under it i guess
mathslover
  • mathslover
a_n represents the last term , here it is 7th term : \(\large a_7 = \textbf{means, 7th term}\)
anonymous
  • anonymous
okay thx
anonymous
  • anonymous
so 7/2 (100 + 7) = 374.5??
anonymous
  • anonymous
am i write @mathslover ?? or no?
anonymous
  • anonymous
right*
mathslover
  • mathslover
No! you don't have :a_7 = 7 see : let the 7th term be : x so i have :\(1330 = \cfrac{7}{2} (100 + x) \) can u solve for x now?
anonymous
  • anonymous
im confused :S
mathslover
  • mathslover
See, we have to calculate the 7th term, right?
anonymous
  • anonymous
yea
mathslover
  • mathslover
Now, I have : \(\large S_n = \cfrac{n}{2} ( a + a_n) \) where S_n = sum of all terms = 1330 (we have calculated it already) a = first term = 100 (given) a_n = nth term = (here n = 7 ) , so a_n = a_7 = 7th term thus , I have : \(\large 1330 = \cfrac{7}{2} ( 100 + a_7) \) Now solve for a_7
anonymous
  • anonymous
so i have to divide 7 and 2 and multiply by 1oo to find a7?
mathslover
  • mathslover
No, see here it is how it goes : \(\large 1330 = \cfrac{7}{2} ( 100 + a_7) \) \(\large 1330 * 2 = 7 (100 +a_7) \space ... \space \textbf{I just multiplied 2 both sides } \) \(\large 2660 = 7(100+a_7)\) \(\large \cfrac{2660}{7} = 100 + a_7 \space ... \space \textbf{Divided 7 both sides}\) \(\large 380 = 100 + a_7 \space ... \space \textbf{as 2660/7 = 380 } \) \(\large{ 380 - 100 = a_7 \space ... \space \textbf{Subtracting 100 both sides}} \) \(\large 280 = a_7 \space ... \space \textbf{as 380 - 100 = 280} \) so the required 7th term is 280
anonymous
  • anonymous
woe this was a confusing, LONG process thanks for bearing with me :/

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