Fanduekisses
  • Fanduekisses
What am I doing wrong?? pls help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Fanduekisses
  • Fanduekisses
Fanduekisses
  • Fanduekisses
I came up with this...?\[\sum_{n=0}^{4}27(\frac{ 1 }{ 9 })^{n}\]
Fanduekisses
  • Fanduekisses
so I'll have to find the sum then square that???

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Fanduekisses
  • Fanduekisses
idk I thought I got it but then I checked the answer key and It wasn't :(
jim_thompson5910
  • jim_thompson5910
You square first, then sum \[\Large (A+B)^2 \ne A^2 + B^2\]
Koikkara
  • Koikkara
hmm, i don't remember how to do it that way... I tried this way, The area of the 1st square = \(27^2 \) After \(÷ 9 \) the area of the center square would be \((27^2)/9\) If repeat once, the area would be\( ((27^2)/9) /9 \) Then if repeat three times, the area would be \((27^2)/(9^4)\)...\(right~~ ?\)
jim_thompson5910
  • jim_thompson5910
and also, 27^2 is not included because the whole 27x27 square isn't shaded
Fanduekisses
  • Fanduekisses
wait, still something weird...
Fanduekisses
  • Fanduekisses
the answer should be 273.88
Koikkara
  • Koikkara
@Fanduekisses i tried this way, In the first step it is applied to an area of 27². and for The 2nd Box, (1/9) of the area to which it is applied. now looking at the second step to the remaining area: 27²-(1/9)27² = (8/9)27². Let us consider, previous unshaded area as A, then an area (1/9)A is added to the shaded area and A-(1/9)A=(8/9)A is left still unshaded. So the shaded areas are: (1/9)27² + (1/9)(8/9)27² + (1/9)(8/9)²27² + (1/9)(8/9)³27² = ? Alternatively, the shaded areas form a Geometric Sequence with a common ratio of (8/9). So the shaded area after 4 steps is just: 27² - (8/9)⁴27² = ? i think so...
Fanduekisses
  • Fanduekisses
I thought I had to us sum of finite geometric series or so, that's what the chapter is about.
Fanduekisses
  • Fanduekisses
So the common ratio is actually 8/9? not 1/9?
Fanduekisses
  • Fanduekisses
:(
jim_thompson5910
  • jim_thompson5910
hmm well I thought it was 8/9, but I keep getting this S = a*(1-r^n)/(1-r) S = 81*(1-(8/9)^6)/(1-8/9) S = 369.406035665294 but it's not the answer your book is saying
Fanduekisses
  • Fanduekisses
:( so confusing. The chapter was on geometric sequences and series.
Fanduekisses
  • Fanduekisses
I thought the common ratio was 1/9.
Fanduekisses
  • Fanduekisses
if 273.88 is the area of the shaded region, then the sum would have to be around 16?
jim_thompson5910
  • jim_thompson5910
each smaller square is 1/9 of the area of the previous bigger square but there are 8 smaller squares added each time, so that's why we get 8*(1/9) = 8/9
Fanduekisses
  • Fanduekisses
How is it related to the topic, geometric series and sequences then? how would I use the summation stuff?
jim_thompson5910
  • jim_thompson5910
you started off with the first term of 81. The largest square area in the center then you add on 8 squares each 3*3 = 9 square units there are 8 of these smaller squares, so 8*9 = 72 square units is added on first term = 81 second term = 72 common ratio = 72/81 = 8/9
jim_thompson5910
  • jim_thompson5910
this pattern repeats where the next term (the sum of the smallest squares in figure 3) is 64 64/72 = 8/9 and so on
Fanduekisses
  • Fanduekisses
ohhhh my God, I was focusing more on the side than on the area!
Fanduekisses
  • Fanduekisses
So using the sum of finite geometric series: \[\frac{ 27(1-(\frac{8 }{ 9 })^4 )}{ 1-\frac{ 8 }{ 9 } }= 273.88\]
Fanduekisses
  • Fanduekisses
:D
jim_thompson5910
  • jim_thompson5910
first term isn't 27
Fanduekisses
  • Fanduekisses
haha yeah I meant 81
jim_thompson5910
  • jim_thompson5910
and you're going to have n = 6 because the problem is showing 3 cases (n=1, n=2, n=3) already and they say repeat the pattern 3 more times
Fanduekisses
  • Fanduekisses
ohh ok thanks so much!

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