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Algebra
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10 Nov 2019

Which of the following arithmetic progressions has 43 terms?

2, 5, 8, 11, …, 212, 215

4, 8, 12, 16, …, 200, 204

1, 6, 11, 16, …, 286, 291

9, 17, 25, 33, …, 337, 345

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Elin Hessel
Elin HesselLv2
17 Apr 2019

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Let S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } S is the universal set. Let sets A and B be subsets of S , where:

Set A = { 5 , 7 , 8 , 9 , 10 , 14 , 15 , 17 , 20 }

Set B = { 2 , 3 , 7 , 11 , 14 , 16 , 20 }

Determine the following:

n ( A ) =

n ( ¯¯¯ A ) =

n ( B ) =

n ( A ∩ B ) =

n ( A ∪ B ) =

PLEASE I NEED HELP

1.Find the sum of this series:–1458+486–162+54–...;7th term.

a. –1586

b. –2186

c. –1094

2.Find the sum of this infinite geometric series: 1000 – 200 + 40 – ...

a. 1250

b. 833 1/3

c. 840

3. The orchestra section of a theater has 26 seats in the front row, 29 seats in the second row, 32 seats in the third row, and so on. The pattern continues until the twelfth row. After that, every row has the same number of seats as row 12. How many seats are there in row 12?

a. 59 seats

b. 36 seats

c. 51 seats

4. Some long-range navigation systems use hyperbolas to determine a ship’s position. Suppose the system imposes coordinates so that the location of a ship is in the first quadrant. A ship is located at the intersection of the hyperbolas with equations 4x^2 – 16y^2 = 64 and 49y^2 – x^2 =81. Find the coordinates of the ship to the nearest hundredth of a unit.

a. (4.96, 1.47)

b. (24.60, 2.16)

c. (1.47, 4.96)

5. Find the common difference for the arithmetic sequence that has 17 as its twelfth term and 71 as its sixth term.

a. –12

b. –18

c. –9

6. Find the arithmetic mean of the terms: a n–1 = 10; a n+1 = 20.

a. 2

b. 15

c. 30

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