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
Stells [14]
3 years ago
6

What is the nth term rule of the quadratic sequence below? 8,14,22,32 ,44, 58, 74...

Mathematics
1 answer:
DanielleElmas [232]3 years ago
8 0

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

You might be interested in
Just a lil some some so please help me
JulsSmile [24]

Answer:

I think its agree. I hope that helped

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
A survey of all planet Umpt found that 36 beings preferred dubble juice to all the other juices. If 40 being were surveyed all t
frozen [14]

Answer:

90%

Step-by-step explanation:

Number of beings that preferred dubble juice to all the other juices = 36

Number of beings surveyed = x

The percentage of people that preferred dubble juice is calculated as:

(Number of beings who preferred dubble juice/Total number of beings surveyed) × 100

36/40 × 100

= 90%

90% of beings preferred dubble juice.

4 0
3 years ago
Alex is working to simplify
stich3 [128]

Answer:

is this all?

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Need help plz help me
forsale [732]
8200? 82,000? 820,000?
4 0
3 years ago
Keith wants to save money to purchase a car. He buys an annuity with quarterly payments that earn 2.8% interest, compounded quar
I am Lyosha [343]

Answer: On each, first identify as a Future Value annuity or Present Value annuity. Then answer the question. 1) How much money must you deposit now at 6% interest compounded quarterly in order to be able to withdraw $3,000 at the end of each quarter year for two years?

Step-by-step explanation: hope this helps

6 0
3 years ago
Other questions:
  • Give one real world example where you would use absolute value.
    11·2 answers
  • if jean and kim combined their weekly allowances they would have $12. Jeans allowance is $2 more than kim’s allowance
    5·1 answer
  • There are 327 official ports of entry in the United States. The Department of Homeland Security selects 15 ports of entry at ran
    9·1 answer
  • The lifetime of a leaf blower is exponentially distributed with a mean of 5 years. If you buy a 12 year old leaf blower, what is
    7·1 answer
  • How many solutions does the following equation have?<br><br> 5k - 9 = 5k + 2
    5·2 answers
  • Mr. Campbell was travelled 80 miles in 2 hours. What was his average speed?
    8·1 answer
  • Helppppppo poooooooo<br>​
    8·1 answer
  • Consider the inequality x + 8 &gt; 13.
    12·2 answers
  • The square root of 20 and 63
    10·2 answers
  • Help A costume designer needs to make 12 costumes for the school play.Each costume requires 2 2/3 yards of fabric.How many yards
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!