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
-Dominant- [34]
2 years ago
8

What is the nth term rule of the quadratic sequence below? 4,15,30,49,72,99,130,...

Mathematics
1 answer:
navik [9.2K]2 years ago
7 0

Answer:

The nth term rule of the quadratic sequence is 2n^{2} +5n-3.

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by =  an^{2}+bn+c

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a  =  \dfrac{4}{2} = 2

SO, the first term of the nth term rule equation is an^{2} = 2n^{2}.

Now, in the term 2n^{2}, put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then 2n^{2} = 2 \times (1)^{2} = 2

If n = 2, then 2n^{2} = 2 \times (2)^{2} = 8

If n = 3, then 2n^{2} = 2 \times (3)^{2} = 18

If n = 4, then 2n^{2} = 2 \times (4)^{2} = 32

If n = 5, then 2n^{2} = 2 \times (5)^{2} = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is 2n^{2} +5n-3.

You might be interested in
If u(x) = x^5 - x^4 + x^2 and v (x) = -x^2 which expression is equivalent to ( u/ v) (x)
yawa3891 [41]

Answer:

(u/v)(x)=-x^{3}+x^{2}-1

Step-by-step explanation:

You have the following functions:

u(x)=x^{5}-x^{4}+x^{2}\\v(x)=-x^{2}

 Therefore (u/v)(x) indicates that you must divide both functions, as you can see below:

(u/v)(x)=\frac{x^{5}-x^{4}+x^{2}}{-x^{2}}

Simplify it. Therefore, you obtain:

(u/v)(x)=\frac{x^{5}-x^{4}+x^{2}}{-x^{2}}\\\\(u/v)(x)=-x^{3}+x^{2}-1

3 0
3 years ago
Read 2 more answers
Calculate and express your answer in decimal form: 1/2 x 17 *
sp2606 [1]

Answer:

8.5

Step-by-step explanation:

5 0
3 years ago
3/8 + 4/8 = ? please help
maksim [4K]
The answer is going to be 7/8. hope that helped
4 0
3 years ago
Read 2 more answers
Speed=60 km/h time= 2 hours 20 minutes, what is the distance?
daser333 [38]

Answer:

26km

Step-by-step explanation:

d=speed × time

d=60×2.33

d= 140km

8 0
3 years ago
Find the volume of the solid.<br> 11 cm<br> 11 cm<br> 11 cm
grin007 [14]

Answer:1331cm

Step-by-step explanation:vol=lbh

11*11*11cm=1331cm

6 0
3 years ago
Other questions:
  • The regression calculator shows the relationship between the hours Devin spent playing a video game, x, and the levels he achiev
    11·1 answer
  • What is 1,002 in expanded form
    15·2 answers
  • I need to know where to plot the points on the graph <br><br>30 points
    10·1 answer
  • Pls help how do you do this
    15·1 answer
  • The volume of the Box 4 inches wide 2 inches high and 5 in long is
    5·2 answers
  • If f(x) = 1/2x^3 + 2x, find f(-2).
    12·2 answers
  • What is the answer to this problem?
    14·2 answers
  • Pls answer this fast
    14·1 answer
  • Can anyone help me please I'm not good at math:(​
    9·1 answer
  • Evaluate: <img src="https://tex.z-dn.net/?f=%5Csqrt%7B100-36%7D%20%2B%2032%20-%201" id="TexFormula1" title="\sqrt{100-36} + 32 -
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!