Question

What am I doing wrong?? pls help!

Answer 1

I came up with this...?\[\sum_{n=0}^{4}27(\frac{ 1 }{ 9 })^{n}\]

Answer 2

so I'll have to find the sum then square that???

Answer 3

idk I thought I got it but then I checked the answer key and It wasn't :(

Answer 4

You square first, then sum

\[\Large (A+B)^2 \ne A^2 + B^2\]

Answer 5

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 \((27^2)/(9^4)\)...\(right~~ ?\)

Answer 6

and also, 27^2 is not included because the whole 27x27 square isn't shaded

Answer 7

wait, still something weird...

Answer 8

the answer should be 273.88

Answer 9

@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...

Answer 10

I thought I had to us sum of finite geometric series or so, that's what the chapter is about.

Answer 11

So the common ratio is actually 8/9? not 1/9?

Answer 12

:(

Answer 13

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

Answer 14

:( so confusing. The chapter was on geometric sequences and series.

Answer 15

I thought the common ratio was 1/9.

Answer 16

if 273.88 is the area of the shaded region, then the sum would have to be around 16?

Answer 17

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

Answer 18

How is it related to the topic, geometric series and sequences then? how would I use the summation stuff?

Answer 19

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

Answer 20

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

Answer 21

ohhhh my God, I was focusing more on the side than on the area!

Answer 22

So using the sum of finite geometric series:
\[\frac{ 27(1-(\frac{8 }{ 9 })^4 )}{ 1-\frac{ 8 }{ 9 } }= 273.88\]

Answer 23

:D

Answer 24

first term isn't 27

Answer 25

haha yeah I meant 81

Answer 26

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

Answer 27

ohh ok thanks so much!