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Karo-lina-s [1.5K]
2 years ago
8

What is the nth term rule of the quadratic sequence below?

Mathematics
1 answer:
Ahat [919]2 years ago
5 0

Answer:

The nth term = n^2 - 2n - 3.

Step-by-step explanation:

Here, we will be finding the nth term of a quadratic number sequence. A quadratic number sequence has nth term = an² + bn + c

Example 1

Write down the nth term of this quadratic number sequence.

-3, 8, 23, 42, 65...

Step 1: Confirm the sequence is quadratic. This is done by finding the second difference.

Sequence = -3, 8, 23, 42, 65

1st difference = 11,15,19,23

2nd difference = 4,4,4,4

Step 2: If you divide the second difference by 2, you will get the value of a.

4 ÷ 2 = 2

So the first term of the nth term is 2n²

Step 3: Next, substitute the number 1 to 5 into 2n².

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Step 4: Now, take these values (2n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

2n² = 2,8,18,32,50

Differences = -5,0,5,10,15

Now the nth term of these differences (-5,0,5,10,15) is 5n -10.

So b = 5 and c = -10.

Step 5: Write down your final answer in the form an² + bn + c.

2n² + 5n -10

Example 2

Write down the nth term of this quadratic number sequence.

9, 28, 57, 96, 145...

Step 1: Confirm if the sequence is quadratic. This is done by finding the second difference.

Sequence = 9, 28, 57, 96, 145...

1st differences = 19,29,39,49

2nd differences = 10,10,10

Step 2: If you divide the second difference by 2, you will get the value of a.

10 ÷ 2 = 5

So the first term of the nth term is 5n²

Step 3: Next, substitute the number 1 to 5 into 5n².

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Step 4: Now, take these values (5n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

5n² = 5,20,45,80,125

Differences = 4,8,12,16,20

Now the nth term of these differences (4,8,12,16,20) is 4n. So b = 4 and c = 0.

Step 5: Write down your final answer in the form an² + bn + c.

5n² + 4n

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A sweater is on sale for 20% off. A jacket is on sale for 15% off. The sale price for each item is $34.00. Which item cost more
SashulF [63]

The sweater cost more originally. It costs $2.50 more from jacket.

Step-by-step explanation:

Given,

Discount rate of sweater = 20%

Sale price of sweater = (100-20)% = 80%

Discount rate of jacket = 15%

Sale price of jacket = (100-15)% = 85%

Sale price of each item = $34.00

Let,

x be the original price of sweater.

y be the original price of jacket.

80% of x = 34

\frac{80}{100}x=34\\0.80x=34

Dividing both sides by 0.80

\frac{0.80x}{0.80}=\frac{34}{0.80}\\x=42.50

The original price of sweater is $42.50

85% of y = 34

\frac{85}{100}y=34\\0.85y=34

Dividing both sides by 0.85

\frac{0.85y}{0.85}=\frac{34}{0.85}\\y=40

The original cost of jacket is $40

Difference = 42.50 - 40 = $2.50

The sweater cost more originally. It costs $2.50 more from jacket.

Keywords: subtraction, division

Learn more about subtraction at:

  • brainly.com/question/10557938
  • brainly.com/question/10600222

#LearnwithBrainly

4 0
3 years ago
Equivalent expression of 10+(x divided 16)
Ivahew [28]

Answer:

x/16 + 10

Step-by-step explanation:

10+(x÷16)

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times 16/16.

10 x 16 / 16 + x/16

Since 10 x 16 / 16 and x/16 have the same denominator, add them by adding their numerators.

10 x 16 + x / 16

Do the multiplications in 10×16+x.

160 + x / 16 = x/16 + 10

4 0
3 years ago
Goods bought for $800 had to be sold off at a loss of 8% the selling price was​
Vikentia [17]

Answer:

8% of 800 is 64

800-64=736

Step-by-step explanation:

4 0
3 years ago
What’s the answer to this problem?
Alja [10]

Answer:

Figure:         Amount of tiles:

1                    5

2                   8

3                   11

4                   14

5                   17

6                   20

7                   23

8                   26

9                   29

10                 32

11                  35

12                 38

13                 41

The sequence/pattern is +3 tiles.

So Figure 13 will have 41 tiles.

I hope this helps!

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>
3 0
3 years ago
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Rudik [331]
B. I am so sorry if it is not right
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3 years ago
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