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
Which counterexample shows that the conjecture "Every parallelogram is also a rectangle" is false?
saveliy_v [14]
A parallelogram without four right angles would prove that to be false.
5 0
2 years ago
Read 2 more answers
Please help me... with at least 3 or 4.
EleoNora [17]

3.right angle
4. Right angle
5 0
2 years ago
Read 2 more answers
Jason had $414 in his savings account. He deposited $125 last week, and then he withdrew $88 from the account this week to buy n
ExtremeBDS [4]

Answer:

B) 451

Step-by-step explanation:

1) 414 + 125 = 539

2) 539 - 88 = 451

4 0
3 years ago
Read 2 more answers
On picture day, 3 times as many girls wore dresses rather than pants. If there are 12 girls in the class, how many wore a dress?
katrin2010 [14]

Answer:

36

Step-by-step explanation:

3 * 12 = 36

if there are 12 girls and 3 times more wore dress then 3 times 12 is 36.

3 0
2 years ago
Read 2 more answers
Angles 1 and 2 form a right angle.Which word describes their measures?
Andreas93 [3]

Answer:

90 degree angle because a right angle is always 90 degrees

6 0
3 years ago
Read 2 more answers
Other questions:
  • Simplificati fractile urmatoare pana cand obtinem fractii ireductibile:
    9·2 answers
  • I NEED HELP ON 15 AND 16 PLEASE HELP ME I DONT UNDERSTAND IT
    13·1 answer
  • 22. Which of the following is recommended as a way to prevent vehicle backover deaths?
    15·1 answer
  • What is the degree of this polynomial? 5/7y3 +5y2 +y +1​
    6·2 answers
  • Help please will give thanks
    15·1 answer
  • Huong is cooking cupcakes. The recipe calls for three and five sixths cups of sugar. She accidentally puts in three and nine eig
    5·1 answer
  • the length and width of the rectangle are in ratio 4:3.If the perimeter of the rectangle is 56 m find the length and width of th
    6·2 answers
  • What is another way to<br> write 48 tens?
    5·2 answers
  • Twenty toothpicks, each 6 cm long, form a figure consisting of six equilateral triangles and a rectangle as shown. What is the t
    9·1 answer
  • A family of 2 adults and 3 children went out to dinner. The total bill was $42. Each child's dinner cost $4. How much did each a
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!