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
raketka [301]
3 years ago
5

The nth term of this sequence is ansquared+by+c 1,11,27,49 Find the values of a b and c

Mathematics
1 answer:
stiv31 [10]3 years ago
4 0

Answer:

The values of a, b and c are:

  • a = 3
  • b = 1
  • c = -3

Step-by-step explanation:

Step 1:

First Confirm the sequence is quadratic by finding the second difference.

Sequence = 1,11,27,49

1st difference:

  • 11-1=10
  • 27-11=16
  • 49-27=22

2nd difference:

  • 16-10=6
  • 22-16=6

Step 2:

Just divide the second difference by 2, you will get the value of a.

6 ÷ 2 = 3

So the first term of the nth term is 3n^{2}

Step 3: Next, substitute the number 1 to 5 into  3n^{2}

n = 1,2,3,4,5

3n² = 3,12,27,48,75

Step 4:

Now, take these values (3n²) from the numbers in the original number sequence and work out the nth term of these numbers that form a linear sequence.

n = 1,2,3,4,5

3n² = 3,12,27,48,75

Differences:

1 - 3 = -2

11 - 12 = -1

27 - 27 = 0

49 - 48 = 1

Now the nth term of these differences (-2,-1,0,1) is (n - 1) - 2.

so b = 1, and c = -3

Step 5: Write down your final answer in the form an² + bn + c.

3n² + (n - 1) -2

= 3n² + n - 1 - 2

= 3n² + n - 3

Therefore, the values of a, b and c are:

  • a = 3
  • b = 1
  • c = -3
You might be interested in
Susan walked for 30 minutes. Reggie walked 3 times longer than Susan.
Fed [463]
The answer is the A :)
30*3 and you'll get the number of minutes Reggie walked
8 0
3 years ago
Can people help me on this please I need it!!! It’s really important
Firdavs [7]

Answer:

62

Step-by-step explanation:

The total of a triangle is 180

so 78+48 is 118

180-118=62

5 0
2 years ago
Gabriel went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 35 grams of sugar and
kupik [55]

Answer:

9 bottles of soda and 7 bottles of juice

Step-by-step explanation:

Let x be the number of bottles of soda purchased and y be the number of bottles of juice purchased.

1. Gabriel purchased 2 more bottles of soda than bottles of juice, then

x=y+2

2. Each bottle of soda has 35 grams of sugar, then there are 35x g of sugar in x bottles of soda.

Each bottle of juice has 10 grams of sugar, then there are 10y g of sugar in y bottles of juice.

In total, there are 35x+10y g of sugar.

All bottles collectively contain 385 grams of sugar, thus

35x+10y=385

3. Solve the system of two equations:

\left\{\begin{array}{l}x=y+2\\ \\35x+10y=385\end{array}\right.

Substitute the first equation into the second equation:

35(y+2)+10y=385\\ \\35y+70+10y=385\\ \\35y+10y=385-70\\ \\45y=315\\ \\y=7\\ \\x=7+2=9

7 0
3 years ago
Read 2 more answers
Felicia put $8500 into a CD that pays 2.8% interest compounded semiannual. According to the rule of 72, approximately how long w
maksim [4K]
<span>25.7 years The rule of 72 is a simple approximation on how long it will take to double your money. You simply divide 72 by the interest rate and you'll have your estimate on the number of years it will take. So 72 / 2.8 = 25.7 years. To demonstrate that it's just an estimate, you can take the log of 2 and divide by the log of 1.028 to get the exact value. This far more complicated calculation gives the result of 25.1 years. And to be honest, the estimate of 25.7 years is more than close enough for such an quick and easy rule of thumb.</span>
5 0
2 years ago
What is the distance from point A to point D on the number line?
mrs_skeptik [129]
The answer would be 3.5
7 0
3 years ago
Other questions:
  • What is the answer for 60x-24= ? Apply the distributive property and the greatest common factor to write an equivalent expressio
    11·2 answers
  • If (6^0)^x = 1 , what are the possible values of x? Explain your answer. (5 points)
    15·2 answers
  • Quincy was stuck inside during an afternoon rainstorm. He spent 20 minutes reading, 18 minutes eating lunch, 12 minutes playing
    12·2 answers
  • Cual es factor de 8​
    7·1 answer
  • Evelyn is making a candy that contains 25% dark chocolate and the rest milk chocolate. The candy has 3 pounds of milk chocolate.
    12·1 answer
  • Solve 4x4 + 7x2 – 2 = 0. Choose the factored form of the polynomial expression.
    6·2 answers
  • Find the solutions to x⁴-64=0 and the x-intercepts of the graph of y=x⁴-64.
    15·1 answer
  • The approximate number of Calories, C, that an animal needs each day is given by C = 72m^3/4, where m is the animal's mass in ki
    10·1 answer
  • 30 POINTS NO CAP PUT REALL STUFF
    11·1 answer
  • -3 divided by -2/5 in fraction form
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!