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
Lisa [10]
3 years ago
12

Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive fo

rmula for a general term in the sequence. Explain in detail how you found both formulas.
Mathematics
2 answers:
Virty [35]3 years ago
7 0

Answer:

Let the first five terms of a sequence be, 4,8,12,20,24

Ok, let me explain the meaning of term explicit and Recursive formula.

Explicit formula ,is the general formula to find any  term of the sequence.

And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.

So,the explicit formula for the sequence is,

y = 4 n, where , n is any natural number.

And the recursive formula is .

y = 4 (n-1), with the help of (n-1)th term we can find nth term.

First term =4=4 × 1

Second term =8 =4 × 2

Third term =12=4×3

Fourth term =16 =4 × 4

.....................

...........................

.................................

(n-1) th term =4 × (n-1)

nth term =4 × n

Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.

As, you said you don't want simpler sequence

Consider the first five terms of the sequence, 0, 3,8,15, 24.

Explicit formula =n² + 2 n

Recursive formula=(n-1)²+2(n-1)

If,you will look at the sequence, it is neither Arithmetic nor geometric .

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

So, Explicit formula= n²+ 2 n, where n is a whole number.

Valentin [98]3 years ago
6 0

Answer: The answer is 5, 10, 20, 40 and 80.

Step-by-step explanation:  We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.

Let the first five terms of a sequence be  5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term a_1 5 and common ratio r=2.

Therefore, we have

a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots

Therefore, the recursive formula is

a_{n+1}=2a_n,~~a_1=5.

And explicit formula is

a_n=a_1r^{n-1}.

You might be interested in
Please help which should I choose
Aleksandr [31]
<h3>Answer: Choice A. Graph (1)</h3>

Reasoning:

If it is at all possible to draw a single vertical line through more than one point on the curve, then the graph is not a function. With graphs (2), (3) and (4), we can draw a vertical line through more than one point on those curves, so they aren't functions. Graph (1) is the only thing left. This graph is a function because it is not possible to draw a single vertical line through more than one point. It passes the vertical line test. Any input (x) leads to exactly one and only one y output.

Nice work on getting the correct answer when you chose "graph (1)".

7 0
3 years ago
It took the carriage 2.5 hours to travel 20 miles. H ow long will it take for the carriage to travel in 12 miles
Tomtit [17]
\bf \begin{array}{ccll}&#10;hours&miles\\&#10;\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\&#10;2.5&20\\&#10;h&12&#10;\end{array}\implies \cfrac{2.5}{h}=\cfrac{20}{12}\implies \cfrac{2.5\cdot 12}{20}=h
6 0
3 years ago
Tonya has a small picture with a length of inches. She wants to enlarge the picture by a factor of 7 and frame it. Which of the
Elena L [17]
Enlarge the picture 7 times by inches
3 0
3 years ago
There were 27,000 people at a ball game in Los Angeles. The day's receipts were $204,000. How many people paid $13 for reserved
Studentka2010 [4]
21000 people paid for general admission and 6000 paid for reserved seats. This is solved by making 2 equations. Out of 27000 people who were at game, x of them paid for general admission and y for reserved seats, thus
x + y = 27000
As said, daily receipts were 204000$. As reserved seat is 13$, y of them gave 13$ each (y*13$) and x of them gave 6 for general admission(x*6) and those two add up and we get second equation
13y + 6x = 204000.
This can be solved by transforming first equation into x = 27000 - y and then replacing the x in second.
13y + 6*(27000 - y) = 204000
13y + 162000 - 6y = 204000
7y = 42000
y = 6000
x + 6000 = 27000
x = 27000 - 6000 = 21000
5 0
3 years ago
B(x)=x+4, what is b(-10)
vovikov84 [41]

Answer:

B(-10)=-6

Step-by-step explanation:

we have

B(x)=x+4

we know that

B(-10) is the value of the function B(x) for the value of x=-10

so

substitute the value of x=-10 in the function

B(-10)=-10+4=-6

therefore

B(-10)=-6

8 0
3 years ago
Other questions:
  • F(x)=3x+2 and g(x)=x exponent 2 minus x . g(2) =
    7·1 answer
  • Sam Collects baseball cards. He currently has 112 cards in his collection. He plans to buy 5 new cards every month, write a verb
    8·1 answer
  • And isosceles triangle has two sides of equal length. The third side is five less than twice the length of one of the other site
    8·1 answer
  • Ben strikes out 90 times in 340 at bat. What percent of the time does Ben strike out
    8·1 answer
  • Find the solutions of the quadratic equation
    8·1 answer
  • Patsy can decorate 3 1/2 cakes in 1/4 hour. At this rate, how many cakes can she decorate in 1 hour?
    6·1 answer
  • Triangles ABC and DEF have the following characteristics:
    14·2 answers
  • Luke invested $2400 in two accounts. The first account pays 3% simple interest. The second account pays 3% compound interest wit
    14·1 answer
  • Serenity has 83.2 ounces of candy left over from Halloween. She want to give each of her friends 1.28 ounces of candy. How many
    9·1 answer
  • Write the equation of the line passing<br> through the point (2, -1) with a slope of -3.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!