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
DENIUS [597]
3 years ago
12

Write down the first 6 elements of the following sequence (where n ∈ Z+), then give a recursive definition for an. Do not forget

the base case. (You do not need to prove it is correct).
a. an - 3n - 10
b. an= (1+(-1)^n)^n
c. an= 2n! (2)
Mathematics
1 answer:
Sonbull [250]3 years ago
5 0

Answer:

a. The first six terms are:

-7, -4, -1, 2, 5, 8

b. The first six terms are:

0, 2, 0, 2, 0, 2.

c. The first six terms are:

4, 8, 24, 96, 480, 2880

Step-by-step explanation:

a. an - 3n - 10

For n = 1

a1 = 3(1) - 10

= -7

For n = 2

a2 = 3(2) - 10

= -4

For n = 3

a3 = 3(3) - 10

= -1

For n = 4

a4 = 3(4) - 10

= 2

For n = 5

a5 = 3(5) - 10

= 5

For n = 6

a6 = 3(6) - 10

= 8

The first six terms are:

-7, -4, -1, 2, 5, 8

b. an= (1+(-1)^n)^n

For n = 1

a1 = (1+(-1)^1)^1

= 0

For n = 2

a2 = (1+(-1)^2)^1

= 2

For n = 3

a3 = (1+(-1)^3)^1

= 0

For n = 4

a4 = (1+(-1)^4)^1

= 2

For n = 5

a5 = (1+(-1)^5)^1

= 0

For n = 6

a6 = (1+(-1)^6)^1

= 2

The first six terms are:

0, 2, 0, 2, 0, 2.

c. an= 2n! (2)

For n = 1

a1 = 2(1!)(2)

= 4

For n = 2

a2 = 2(2!)(2)

= 8

For n = 3

a3 = 2(3!)(2)

= 24

For n = 4

a4 = 2(4!)(2)

= 96

For n = 5

a5 = 2(5!)(2)

= 480

For n = 6

a6 = 2(6!)(2)

= 2880

The first six terms are:

4, 8, 24, 96, 480, 2880

You might be interested in
The entertainment sports industry employs athletes, coaches, referees, and related workers. Of these, 0.35 work part time and 0.
Alona [7]
<h2>0.87</h2>

Step-by-step explanation:

let A be the event that employees work full time

Pr(A) =  1 - 0.35=  0.65   (  given : Pr( employee work part time) = 0.35)

let B be the event that employees earn more than $20,540

Pr(B) =  0.52

Pr(  employee work full time and earn more than $20,540) =  0.3

Pr( A∩B) = 0.3

we know that

Pr( employee work full time or earn more than $20,540) = Pr( A∪B)

Also

Pr( A∪B)   =  Pr(A)  + Pr(B)  -  Pr(A∩B)

                   =  0.65   + 0.52  -   0.3

                    =    1.17    -   0.30

                     =    0.87

7 0
3 years ago
Estimate 8/9 + 4/7<br> Sum or difference
BlackZzzverrR [31]
8/9 + 4/7=1 29/63 ESTIMATE:2
8/9 - 4/7=<span>20/63 ESTIMATE:0

</span>

6 0
3 years ago
112 students are going on a field trip. If each bus can take 50 students, how many busses are needed?
MrRissso [65]

Answer:

3 buses are needed.

Step-by-step explanation:

If there are only 2 buses, it would be full, but there would still be 12 students without a bus. To take all students, you'd need 3 buses. 2 buses will be full, and the other bus would only have 12 students.

8 0
3 years ago
Read 2 more answers
2+2? I don’t know the answer I am in first grade
geniusboy [140]

Answer: 4

Step-by-step explanation: I don't think you are in 1st grade but if you are here you go.

7 0
3 years ago
Read 2 more answers
How do you solve algebraically 8x^2=18
vodka [1.7K]
That would be
x =  + \frac{ \sqrt[]{3} }{ \sqrt[]{2} }
BTW the plus sign is supposed to have this sign underneath it _
Good luck.
5 0
3 years ago
Other questions:
  • Victoria, Wanda, and Yvonne went out for a meal together. When the bill came, they thought they would divide it equally between
    10·1 answer
  • Factor out gcf <br> 16x5 – 12x3
    8·1 answer
  • Two rectangles have the same width. The length of one is 1 foot longer than the width. The length of the other is 2 feet longer
    5·1 answer
  • Write an equation of the line that passes through a pair of points (5, -2) , (4,5)
    8·1 answer
  • A 4.3 ounce tomato has about 24 calories how many calories are in one ounce
    9·1 answer
  • IN NEED OF HELP PLEASE !!! <br> ALSO EXPLAIN PLEASE
    9·1 answer
  • What is the shape of the base of a pentagonal right prism?
    15·1 answer
  • Pls help with question.
    7·1 answer
  • A cell phone provider offers a plan that costs $20 per month plus $0.20 per text message sent or received. A comparable plan cos
    14·2 answers
  • PLEASE ANSWER THIS ASAP!!!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!