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
In​ 2000, 49 %49% of the residents in a large city regularly used newspapers for getting news and this has decreased at an avera
kogti [31]

Answer:

  P(x) = -1.1x +49

Step-by-step explanation:

You are given the percentage in 2000 (for x=0) as 49, and told that its rate of change is -1.1 percent per year. So, with a slope of -1.1 and an intercept of 49, the slope-intercept form of the linear equation becomes ...

  P(x) = -1.1x +49

_____

The slope-intercept form for slope m and y-intercept b is ...

  y = mx + b

7 0
3 years ago
Kara ate 2 7/9 of the raisins she packed. Which box shows the decimal equivalent of the amount of raisins she ate? Box A: 2.777
vivado [14]

Answer:  Box A, 2.777

=======================================================

Explanation:

When using a calculator or long division, you should find that

7/9 = 0.7777...

where the 7s go on forever

So we can say that 7/9 = 0.777 approximately. You could argue that the last '7' would round up to an '8' and we could say 7/9 = 0.778; however, I'll stick to the first value so that it matches with the answer.

Since 7/9 = 0.777, this means 2 & 7/9 = 2 + 7/9 = 2 + 0.777 = 2.777 which is box A.

6 0
3 years ago
(Y = x - 3), (y = -3/5x + 5)
saul85 [17]

Answer:

(5,2)

Step-by-step explanation:

i am unsure of what your question is but if you want the point of intersection of the two lines its (5,2)

7 0
3 years ago
Arrange the events in Polish history in chronological order using the numbers 1-6.
Basile [38]

Answer:

3

5

1

2

4

6

Yan po para sa akin.

4 0
3 years ago
Read 2 more answers
Simple the expression <br> ( 3k + 4 1/5) + 8 3/5
lesantik [10]

Answer:

3k+12\frac{4}{5}

Step-by-step explanation:

(3k+12\frac{4}{5})

Convert mixed numbers to improper fractions:

a\frac{b}{c}=\frac{a*c+b}{c}

4\frac{1}{5}=\frac{4*5+1}{5}

=\frac{21}{5}

=(3k+\frac{21}{5} )+\frac{43}{5}

Add the fractions

\frac{21}{5}+\frac{43}{5}

\frac{21}{5} \frac{43}{5} =\frac{64}{5}

=3k+\frac{64}{5}

Divide 64 by 5

\frac{64}{5}12.8 or 12\frac{4}{5}

=3k+12\frac{4}{5}

7 0
2 years ago
Other questions:
  • Add 6/7 + 80/9 . Enter your answer below as an improper fraction in lowest terms, using the slash ( / ) as the fraction bar.
    15·2 answers
  • Fathi has $1.10 , in his printing account. Each sheet of paper he uses reduces his printing account balance by $0.25. Fathi want
    7·1 answer
  • What is the rule help I’m to stupid
    7·1 answer
  • Find dy/dx by differentiating implicitly <br> x^2y+3xy^3-x=3
    6·1 answer
  • Amanda is mailing 5 remote control cars. The mass has a total of 3,470 grams, What is the mass of each car?
    5·1 answer
  • Evaluate the expression for v=1.<br><br><br>4[v]+15[ ]
    15·1 answer
  • Can someone help me please?
    9·1 answer
  • Write an equivalent expression.
    9·1 answer
  • consider the series ∑n=1[infinity]4n 2. let sn=∑i=1n4i 2 be the n-th partial sum; that is the sum of the first n terms of the se
    8·1 answer
  • Which statement could be used in step 2 when proving
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!