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
Margaret [11]
3 years ago
10

Work out the formula of the nth term in the following quadratic sequence: 19, 15, 9, 1...

Mathematics
1 answer:
Butoxors [25]3 years ago
6 0

In a quadratic sequence we'll get a linear first difference and a constant second difference.  Let's verify that.

n          1   2   3   4

f(n)       19  15  9   1

1st diff   -4  -6  -8

2nd diff     2   2

We see that we got a constant second difference.  We could just extend that and work back up to get more values.

n          1   2   3   4       5    6      7

f(n)       19  15  9   1      -9   -21   -35

1st diff   -4  -6  -8   -10  -12   -14

2nd diff     2   2    2     2    2

That's just an aside; we're after the general formula.  We have

f(1)=19, f(2)=15, f(3)=9

In general we can assume

f(n) = an²  + bn + c

We get three equations in three unknowns,

19 = a(1²)+b(1)+c = a+b+c

15 = a(2²) + b(2) + c = 4a + 2b + c

9 = a(3²) + b(3) + c =  9a + 3b + c

That's a 3x3 linear system; it's easy to solve directly.  Subtracting pairs,

4 = -3a - b

6 = -5a - b

Subtracting those,

-2 = 2a

a = -1

b = -3a -4 = -1

c = 19-a-b = 21

Answer: f(n) = -n² - n + 21

Check:

f(1) = -1 - 1 + 21 = 19, good

f(2) = -4 - 2 + 21 = 15, good

f(3) = -9 - 3 + 21 = 9, good

f(4) = -16 - 4 + 21 = 1, good

Let's check our extended table, how about

f(7)= -49 - 7 + 21 = -35, good

You might be interested in
Luke wants to reduce the area of his rectangular Garden by 1/4 the expression 14/W can be used to represent this change. What is
Naddika [18.5K]

Answer:

The another way to write the expression i: \frac{7}{2W}.

Step-by-step explanation:

We have been given Luke wants to reduce the area of his rectangular Garden by 1/4 the expression 14/W.

Mathematically, \frac{1}{4}\cdot \frac{14}{W}

The other way to write it is in its simplified form which is:

\frac{1}{2}\cdot \frac{7}{W}

\frac{7}{2W}

The another way to write the expression is: \frac{7}{2W}

4 0
3 years ago
What is the value of 2|2-9|-3(4+2)?<br> A. -32<br> B. -26<br> C. -15<br> D. -5 <br> E. -4
Nataly [62]
Simplify
2(7)-3(6)
= 14-18 = -4
3 0
2 years ago
What is the difference between 76.82 and 2.761?<br> 49.210<br> 74.679<br> 74.059<br> 79.581
dsp73
The difference would be 74.059
3 0
3 years ago
Please Help !<br> Answer the questions about Figure A and Figure B below.
Flauer [41]

Answer:yes

Step-by-step explanation:

Each of their corners are at a 90* angle

8 0
3 years ago
Can someone help with #17
iVinArrow [24]
B, Because to be a parallelogram it has to have two sides that are both parallel and congruent
8 0
2 years ago
Other questions:
  • If 24 extra large cans of soup will serve 96 people, how many cans should Ann buy to serve 28 people?
    12·1 answer
  • How many cg/m² is 0.0044 mg/mm²?
    9·1 answer
  • A) 1<br> b) -20<br> c) 20<br> d) 7
    9·1 answer
  • Create the quadratic function that contains the points (0-2), (1, 0) and (3, 10). Show all of your work for full credit.
    12·1 answer
  • (19x² + 12x+12) + (7X2 + 10x +13)
    12·1 answer
  • What is the slope of the line that passes through the points (-3, -9)(−3,−9) and (22, -4) ?(22,−4)? Write your answer in simples
    11·1 answer
  • A rectangular sticker has an area of 10 square centimeters. the function f(x) = 10/x models the width f of the sticker, in centi
    12·1 answer
  • Fide f (-7) evaluate the function
    8·1 answer
  • PERSON WHO GETS RIGHT ILL GIVE BRAINLIEST! Which values from the given replacement set make up the solution set of this inequali
    8·1 answer
  • If 5a+b=14 then a = what<br> explain how you got it pls
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!