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Oliga [24]
2 years ago
13

What is the nth term of the sequence -2 -8 -18 -32 -50

Mathematics
1 answer:
andreev551 [17]2 years ago
6 0

Answer:

-2n²

Step-by-step explanation:

Using the image attached:
We see that the second differences (blue ones) are all equal so we conclude that this is a quadratic sequence.
The quadratic sequence has the form:
T_{n} = an^{2}  +bn +c

To find the value of a we just divide second difference ( -4 ) by 2:

  • a = \frac{-4}{2}= -2

Now we have:

  • T_{n}= -2n^{2}  +bn+c

Substitute n_{1} and n_{2} into the equation above:

  • T_{1} = -2(1)^{2}  +b(1) +c
  • T_{2} = -2(2)^{2}  +b(2)+c

Since T_{1} = -2 and T_{2} = -8 , after simplification we have:

  • b +c =0
  • 2b+c=0

The solution of this system is:

  • b=0, c =0

The general term is :

T_{n} = -2n^{2}

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Someone can help me with 31 & 33? i need help
nika2105 [10]

31. It gives you the equation f(x) = -2x + 4 and asks you to solve for f(12). To solve this you must replace x in the equation -2x + 4 with 12 like so:

-2(12) + 4

Remember that when solving this use your rules of PEMDAS. In this case you will first multiply -2 and 12 then add the product with 4

-24 + 4

f(12) = -20

33. Replace x in the equation x³ - x with 5 like so...

5³ - 5

Again, remember to use the rules of PEMDAS to solve this. First take the cube of 5 then subtract 5 from the answer

125 - 5

g(5) = 120

Hope this helped!

~Just a girl in love with Shawn Mendes

3 0
3 years ago
Read 2 more answers
Which of the following is equivalent to the equation -5(3x -8 )= -45 ?
Elan Coil [88]
Distributive property is
a(b+c)=ab+ac so
first, distribute
remember than (-) times (-)=(+)
-5(3x-8)=(-5)(3x)+(-5)(-8)=-15x+(+40)=-15x+40

so it is -15x+40=-45

the answe ris B
4 0
3 years ago
How do I solve this proportional & non proportional functions?
Nikolay [14]
Boy im a about to roast you 
3 0
3 years ago
Which best explains why students who can solve problems create better projects?
Aleksandr-060686 [28]

Answer:

the answer is D

hope its helpful

4 0
3 years ago
Read 2 more answers
Cole wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 4 5 6 ft by 2 1 3 ft. Fi
Shtirlitz [24]

Answer:

Area = 49\frac{25}{36}

Step-by-step explanation:

Given

Tile

Length = 4\frac{5}{6}

Width = 2\frac{1}{3}

See attachment for dimension of the floor

Required

Determine the area covered by the carpet

From the attachment, the dimension of the floor is:

Length = 12\frac{1}{4}

Width = 5

Calculate Area

Area = Length * Width

Area = 12\frac{1}{4} * 5

Area = 61\frac{1}{4}

The area of the tiles is:

Area = 4\frac{5}{6} * 2\frac{1}{3}

Area = \frac{29}{6} * \frac{7}{3}

Area = \frac{203}{18}

Area = 11\frac{5}{18}

So, the carpet area is:

Area = Floor\ Area - Tile\ Area

Area = 61\frac{1}{4} - 11\frac{5}{18}

To improper number

Area = \frac{245}{4} - \frac{208}{18}

Take LCM

Area = \frac{2205 - 416}{36}

Area = \frac{1789}{36}

Area = 49\frac{25}{36}

7 0
3 years ago
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