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4 years ago

15

Each row in a window display of compact disk cartons contains two more boxes than the row above. The first row has one box. Comp

lete the table to find the number of rows in a display containing 144 boxes.

2 answers:

elixir [45]4 years ago

8 0

Hey there!

You know that the pattern increases by 2 each time so just add two each time until you get to 144

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 +23 = 144

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12

So there will be 12 rows in the display

Hope this helps!

~~Cutelion918~~

kherson [118]4 years ago

3 0

The pattern increases by 2 each time.

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 +23 = 144

R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12

There are 12 rows in the display.

I hope this helped! c:

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4 years ago

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations

ivann1987 [24]

Aurora's plan is an illustration of a geometric sequence.

The recursive function is $T_n = 2 T_{n-1$ .
She will complete the 8th station in 512 minutes

From the question, we have:

$(x,y) = \{(1,4),(2,8),(3,16),(4,32)\}$

<u>(a) The pattern model</u>

To check if it represents an arithmetic sequence, we calculate the common difference between the y-coordinates

$d = 8 - 4 = 4$

$d = 16 - 8 = 8$

$d = 32 - 16 = 16$

The calculated differences are not the same;

This means that, the model is not arithmetic

To check if it represents a geometric sequence, we calculate the ratio between the y-coordinates

$r = \frac 84 = 2$

$r = \frac{16}8 = 2$

$r = \frac{32}{16} = 2$

The calculated ratios are the same;

This means that, the model is geometric

<u>(b) The recursive function</u>

The sequence is given as: $(x,y) = \{(1,4),(2,8),(3,16),(4,32)\}$

Where:

$T_1 = 4$

$T_2 = 8$

$T_3 = 16$

$T_4 = 32$

Rewrite as:

$T_1 = 4$

$T_2 = 2 \times 4$

$T_3 = 2 \times 8$

$T_4 = 2 \times 16$

Substitute $T_3 = 16$ in $T_4 = 2 \times 16$

$T_4 = 2 \times T_3$

Express 3 as 4 - 1

$T_4 = 2 \times T_{4-1$

Represent 4 as n

$T_n = 2 \times T_{n-1$

Hence, the recursive sequence is:

$T_n = 2 T_{n-1$

<u>(c) The explicit formula</u>

In (a), we have:

$r =2$

$T_1 = 4$

The nth term of a geometric sequence is:

$T_n = T_1 \times r^{n-1}$

So, we have:

$T_n = 4\times 2^{n-1}$

Express 4 as $2^2$

$T_n = 2^2\times 2^{n-1}$

Apply law of indices

$T_n = 2^{2+ n-1}$

$T_n = 2^{2-1+ n}$

$T_n = 2^{1+ n}$

So, the time to complete the 8th station is:

$T_8 = 2^{1+ 8}$

$T_8 = 2^{9$

$T_8 = 512$

Hence, she will complete the 8th station in 512 minutes

Read more about geometric sequence at:

brainly.com/question/11266123

4 0

2 years ago

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