1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
A family has 5 children. Compute the probabilities of the following events:
Arlecino [84]
I think the answer is 10% and 90%
4 0
3 years ago
Read 2 more answers
Consider an arbitrary ellipse x 2 a 2 + y 2 b 2 = 1. (Assume a, b > 0.) (a) Find a parametrization of the ellipse using the d
uysha [10]

Answer:

α(t) = (-a*Sin(t), b*Cos (t))    where t ∈ [0, 2π]

Step-by-step explanation:

Given an arbitrary ellipse (x²/a²) + (y²/b²) = 1       (a, b > 0)

The parametrization can be as follows

x = -a*Sin(t)

y = b*Cos (t)

then

α(t) = (-a*Sin(t), b*Cos (t))    where t ∈ [0, 2π]

If  t = 0

α(0) = (-a*Sin(0), b*Cos (0)) = (0, b)

If  t = π/2

α(π/2) = (-a*Sin(π/2), b*Cos (π/2)) = (-a, 0)

If  t = π

α(π) = (-a*Sin(π), b*Cos (π)) = (0, -b)

If  t = 3π/2

α(3π/2) = (-a*Sin(3π/2), b*Cos (3π/2)) = (a, 0)

If  t = 2π

α(2π) = (-a*Sin(2π), b*Cos (2π)) = (0, b)

We can see the sketch in the pic.

7 0
3 years ago
Read 2 more answers
Helppppp mereeeeeeeeeee
Vera_Pavlovna [14]

Answer:

A. (x-5)(x-7)

B. It means the zeroes of the graph are at (5,0) and (7,0)

Step-by-step explanation:

A

find what + what equals -12, and multiples to 35.

List all multiples of 35.

1 35

<em>5 7</em>

- 12 is negative so that means it is -5 and -7

(x-5)(x-7)

B

The factor numbers are where the zeroes on a graph are, <u>but</u> whatever is in parenthesis, the number is opposite on a graph (e.g. if it was (x-3), the zero would be (3,0)

4 0
3 years ago
HELP PLEASE!!!!!!!!!!!!
Bogdan [553]

Answer:

See the explanation.

Step-by-step explanation:

We are given the function f(x) = x² + 2x - 5

Zeros :

If f(x) = 0 i.e. x² + 2x - 5 = 0

The left hand side can not be factorized. Hence, use Sridhar Acharya formula and  

x= \frac{-2+\sqrt{2^{2}-4\times(-5)\times1 } }{2} and  

x= \frac{-2-\sqrt{2^{2}-4\times(-5)\times1 } }{2}

⇒ x = -3.45 and 1.45

Y- intercept :

Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.

Maximum point :

Not defined

Minimum point:  

The equation can be expressed as (x + 1)² = (y + 5)

This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis

Therefore, the minimum point is (-1,-5)

Domain :  

x can be any real number

Range:  

f(x) ≥ - 6

Interval of increase:

Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.

Therefore, interval of increase is +∞ > x > -1

Interval of decrease:

-∞ < x < -1

End behavior :  

f(x) = x^{2} +2x-5 =x^{2}  (1+\frac{2}{x} -\frac{5}{x^{2} } )

So, as x tends to +∞ , then f(x) tends to +∞

And as x tends to -∞, then f(x) tends to +∞. (Answer)

7 0
3 years ago
If f(x) = x and g(x) = 2, what is (f o g)(x)?<br> 2x<br> 2<br> x + 2<br> x/2
arlik [135]
(f \circ g)(x)=2
8 0
3 years ago
Other questions:
  • Which fraction has a value thats equal to 7/8? <br> A) 49/64<br> B) 21/24<br> C) 15/8<br> D) 56/8
    12·1 answer
  • What is the value of x in 40,000 mg = 10x g? Please answer quick!
    8·1 answer
  • Which number sentences show ways to solve the problem?
    12·1 answer
  • Autry made 45% of the shots he took during the basketball game. If he attempts 20 shots how many times did he score?
    12·1 answer
  • What is 2 x 2 someone please help
    7·2 answers
  • Which point is located on the x-axis?
    13·2 answers
  • Help Plz I will mark Brainliest
    6·2 answers
  • Which of the following has an exact cube root?<br> a. 125<br> b. 49<br> C. 24
    6·1 answer
  • (3 x 7) + (3 x 5) is the same as
    11·1 answer
  • 4.5 is 75% of what number
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!