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
Marianna [84]
1 year ago
11

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

Mathematics
1 answer:
Vladimir [108]1 year ago
6 0

Answer:

3n² + 5n - 2

Step-by-step explanation:

<u>Given sequence</u>:

6, 20, 40, 66, 98, 136, ...

Calculate the <u>first differences</u> between the terms:

6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136

As the first differences are not the same, calculate the <u>second differences:</u>

14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38

As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.

The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.

Therefore, the n² term is:  3n²

Compare 3n² with the given sequence:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

The second operations are different, therefore calculate the differences <em>between</em> the second operations:

3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18

As the differences are the same, we need to add 5n as the second operation:

\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2  +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2  &-2  & -2  \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

You might be interested in
How much string would you need to go around of a hat shaped like a cone if the radius is 4 inches? ( Use 3.14 for pi)
Paul [167]
The answer is b. 25.12
because we are finding the amount of rope to go around the circle, we are looking for the circumfrence of the circle, and the formula for the circumfrence of the circle is diameter(pi). because the radius of the circle is 4 inches, the diameter iss 8 inches because the diameter is 2(radius) and using multiplication, we can find the the circumfrence to be 25.12 inches
5 0
3 years ago
Read 2 more answers
Which one is a better deal?
saul85 [17]
12 pack is a better deal
5 0
3 years ago
There are 31 football teams with 11 players on each team. How many players are there in all?
Igoryamba

Answer:

341 players

Step-by-step explanation:

31 x 11

= 341 players

5 0
3 years ago
I need help right now​
Neko [114]
In Which Subject I Can Help You In?!
3 0
3 years ago
Read 2 more answers
PLEASE HELP IM BEHIND AND SCHOOL IS OUT IN 2 DAYS
Alexxx [7]

Answer: #1 his school is out

Step-by-step explanation: #2 bcuz all sides equal to 66cm.

Please mark me brainlest.✌✌

5 0
3 years ago
Other questions:
  • PLZZZZZ NEED HELP!!!!!!
    8·1 answer
  • Martin charges $10 for every 5 bags of leaves he
    9·2 answers
  • Someone help plzzz <br> With work if u may plz
    10·1 answer
  • Shannon is paid £1150 a month after deductions.
    13·1 answer
  • Someone help me!!!!!​
    5·1 answer
  • (x+16)²=12 plz help me and show work
    7·1 answer
  • A delivery truck is transporting boxes of two sizes: large and small. The combined weight of the large box and a small box is 70
    12·1 answer
  • ASAP <br><br>options: <br>left<br>right<br>up <br> down​
    5·1 answer
  • Một ông 43 tuổi đến khám tổng quát. Phân tích nước tiểu thấy có đường niệu. Bạn vừa biết có một test T dung phát hiện bệnh tiểu
    5·1 answer
  • A radio tower has a 64 ft Shadow cast by the sun. If the angle from the tip of the shadow to the top of the tower is 78.5°. what
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!