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Mkey [24]
3 years ago
13

7) Write an equation for the tile pattern and use it to find out how many tiles will there be in figure 32?

Mathematics
1 answer:
Dafna11 [192]3 years ago
7 0

9514 1404 393

Answer:

  98

Step-by-step explanation:

The numbers of tiles are 5, 8, 11. This is an arithmetic sequence with a first term of 5 and a common difference of 3. The n-th term is ...

  an = a1 +d(n -1)  . . . . . for first term a1 and common difference d

This sequence has n-th term ...

  an = 5 +3(n -1)

Then the 32nd term is ...

  a32 = 5 + 3(32 -1) = 5 +93 = 98

Figure 32 will have 98 tiles in it.

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A table costs $50 more than a chair. The cost of 6 chairs and 1 table is $750. The equation 6x + x + 50 = 750, where x is the co
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3 years ago
Please help me, thank you!
dlinn [17]

Answer:

a. The first four terms are -4 , -4/3, -4/9 , -4/27

b. The series is converge

c. The series has sum to ∞ , the sum of the series is -6

Step-by-step explanation:

* Lets revise the geometric series

- Geometric series:

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2)

# 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5)

* General term (nth term) of a Geometric Progression:

- U1 = a  ,  U2  = ar  ,  U3  = ar2  ,  U4 = ar3  ,  U5 = ar4

- Un = ar^n-1, where a is the first term , r is the constant ratio

 between each two consecutive terms  and n is the position of the

  number in the sequence

* In the problem

∵ The Un = -4(1/3)^n-1

∴ a = -4

∴ r = 1/3

a) To find the first four numbers use n = 1, 2 , 3 , 4

∴ U1 = a = -4

∴ U2 = -4(1/3)^(2 - 1) = -4(1/3) = -4/3

∴ U3 = -4(1/3)^(3 - 1) = -4(1/3)^2 = -4(1/9) = -4/9

∴ U4 = -4(1/3)^(4 - 1) = -4(1/3)^3 = -4(1/27) = -4/27

* The first four terms are -4 , -4/3, -4/9 , -4/27

b) If IrI < 1  then the geometric series is converge and if IrI > 1

   then the geometric series is diverge

∵ r = 1/3

∴ The series is converge  

c. The convergent series has sum to ∞

- The rule is: S∞ = a/(1 - r)

∴ S∞ = -4/(1 - 1/3) = -4/(2/3) = -4 × 3/2 = -6

* The sum of the series is -6

7 0
3 years ago
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