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
nika2105 [10]
1 year ago
8

Find the nth term of this quadratic sequence 3, 11, 25, 45, .

Mathematics
1 answer:
Hoochie [10]1 year ago
6 0

The term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Given,

In the question:

The quadratic sequence is :

3, 11, 25, 45, ...

To find the nth term of the quadratic sequence.

Now, According to the question;

The first term of the sequence is 3, the second term is 11, the third term is 25, and the fourth term is 45.

The difference between the first and second terms can be calculated as follows:

11-3 = 8

The difference between the second and third terms can be calculated as follows:

25-11 = 14

The difference between the third and fourth terms can be calculated as follows:

45-25 = 20

The sequence is expressed as follows:

3,3+8,11+11,25+20,...

The difference between consecutive terms expands by 6.

Use the principle of mathematical induction.

6(\frac{n(n+1)}{2} )

= 3n(n+1)

The sequence's nth term can be calculated as follows:

term = 3n(n+1) - 4n + 1

             = 3n² - n + 1

Hence, the term of the given quadratic sequence is found to be 3n² - n + 1 using the principle of mathematical induction.

Learn more about Principle of mathematical induction at:

brainly.com/question/29222282

#SPJ1

You might be interested in
The distance from Antville to Beetleton is 60 km.
serious [3.7K]

Answer:

i. Time = 2 hours.

ii. Average speed for the whole journey = 25 km/h

Step-by-step explanation:

Distance from Antville to Beetleton = 60 km

Mr. Caterpillar's speed = 30 km/h

Speed = \frac{distance}{time}

⇒ time = \frac{distance}{speed}

            = \frac{60}{30}

            = 2

time = 2 hours

It would take Mr. Caterpillar 2 hours to travel from Antville to Beetleton at that speed.

On his return journey, his average speed is 20 km/h. Therefore;

average speed for the whole journey = \frac{30 + 20}{2}

                                                 = \frac{50}{2}

                                                 = 25

average speed for the whole journey = 25 km/h

8 0
3 years ago
If 40% of x + 20% of x + 1/10 = 75% of x, then find the value of x. Please give answers with steps
tatyana61 [14]

Answer:

x = 13/12

Step-by-step explanation:

explain on image

3 0
2 years ago
Read 2 more answers
Javier used the expression below to represent his score in a game of mini-golf.
strojnjashka [21]

Simplify by combing like terms to get 2x+5

The answers would be:

the coefficient is 2

the constant is 5

There are two terms.

6 0
3 years ago
Read 2 more answers
By treating savings as an ___ it guarantees that you will save the money instead of spending it
Mekhanik [1.2K]

Answer:

Money market account. I think.. not sure...

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
There are two college entrance exams that are often taken by students, Exam A and Exam B. The composite score on Exam A is appro
elena55 [62]

Answer:

B.The score on Exam A is better, because the percentile for the Exam A score is higher.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Two exams. The exam that you did score better is the one in which you had a higher zscore.

The composite score on Exam A is approximately normally distributed with mean 20.1 and standard deviation 5.1.

This means that \mu = 20.1, \sigma = 5.1.

You scored 24 on Exam A. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{24 - 20.1}{5.1}

Z = 0.76

The composite score on Exam B is approximately normally distributed with mean 1031 and standard deviation 215.

This means that \mu = 1031, \sigma = 215.

You scored 1167 on Exam B, s:

Z = \frac{X - \mu}{\sigma}

Z = \frac{1167 - 1031}{215}

Z = 0.632

You had a better Z-score on exam A, so you did better on that exam.

The correct answer is:

B.The score on Exam A is better, because the percentile for the Exam A score is higher.

3 0
3 years ago
Other questions:
  • 0.4(3k – 0.6)<br> plz help
    5·1 answer
  • A poll asked 15 men in two age groups, 30 and younger and older than 30, whether they had facial hair (mustache, beard, sideburn
    6·1 answer
  • Solve the equation -5x + 2 = 67
    5·2 answers
  • Brennan made lemonade for the county fair. He has 12 Containers of the same size to fill. It takes 16 gallons of lemonade to fil
    9·1 answer
  • 30 POINTS HELP PLEASE
    6·2 answers
  • What is 19 times 45
    13·2 answers
  • Simplify the expression below.
    15·2 answers
  • A dance group from Round Rock High School is fundraising to travel to a competition. The competition entry fee is only $300 for
    9·1 answer
  • Find the value of the expression: 2xy+2x^2 for x=−2.5 and y=−7.5
    11·1 answer
  • Jennifer is checking Megan's homework. They disagree on the answer to this problem: 42 x 22 Jennifer says the product is 32 and
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!