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
Eva8 [605]
3 years ago
12

For each of these lists of integers, provide a simple formula orrule that generates the terms of an integer sequence that begins

with the given list. Assuming that your formula or rule is correct,determine the next three terms of the sequence.
b) 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ...
c) 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,...
d) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, ...
f) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425,...
g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, ...
Mathematics
2 answers:
Anuta_ua [19.1K]3 years ago
8 0

Answer:

b) next three terms of the sequence are 47, 51, 55

c) The next three terms are 1100, 1101, 1110

d) The next three items in the sequence are therefore, 8,8,8

f) The next three terms are 654729075, 13749310575, 316234143225

g) Therefore the next three items in the sequence are 0,0,0

Step-by-step explanation:

b)7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ...

the common difference, d = T_{2} - T_{1} = 11 - 7 = 4

a_{n} = a_{n-1} + 4

43 + 4 = 47

47 + 4 = 51

51 + 4 = 55

next three terms of the sequence are 47, 51, 55

c)  1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,...

Each of these terms are binary numbers of 1,2,3,4........

The 1st next term is the 12th term = 1100₂

The second next term  is the 13th term = 1101₂

The third next term is the 14th term = 1110₂

The next three terms are 1100, 1101, 1110

d)  1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, ...

1 is repeated 1 time , 2 is repeated 3 times, 3 is repeated 5 times, 5 is repeated 7 times, the next number will sure be repeated 9 times( the repetition follows an odd number pattern)

To know the next number that will be repeated 9 times:

1+2 = 3

2+3 = 5

3 + 5 = 8

The pattern is that the previous summation adds to the preceding number

The next three items in the sequence are therefore, 8,8,8

f)  1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425,...

The above sequence follows the pattern a_{n} = a_{n-1} (2n -1)\\

The next three terms are the 10th, 11th and 12th terms

a₁₀ = 34459425((2*10)-1)

a₁₀ = 654729075

a₁₁ = 654729075((2*11)-1)

a₁₁ = 13749310575

a₁₂ = 13749310575((2*12)-1)

a₁₂ = 316234143225

The next three terms are 654729075, 13749310575, 316234143225

g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,...

The sequence changes between 1 and 0. 6 zeros are expected next

Therefore the next three items in the sequence are 0,0,0

Westkost [7]3 years ago
3 0

Answer:

b) T_{n} = 3 + 4n

c) T_{n} = n_{2}

d) T_{n} = n

f) T_{n} = \pi ^{n}_{i=1} (2i - 1)

g) T_{n} = a^{n} : = \left \{ {{a=0} if n is even \atop {a=1} if n is odd } \right.

Step-by-step explanation:

B) 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ...

a = 7

difference  = 4

this is an Arithmetic progression

T_{n} = a + (n  - 1)d

  = 7 + 4(n - 1)

T_{n} = 3 + 4n

the next three terms are 47, 51, 55

C)  1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,...

Given n >0 and n are integers

T_{n} = n_{2}

the result is converted to base 2

the next three terms of the sequence are 1100, 1101, 1110

D) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, ...

this is a square root of prime sequence where each number is repeated (2n -1) times

T_{n} = n

the next three terms of the sequence are 7^{13},  9^{17},  13^{21}.

F) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425,...

T_{n} = \pi ^{n}_{i=1} (2i - 1)

the next three term are

654729075, 1.374931058 x 10^10, 3.162341432 x 10^11

G) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, ...

T_{n} = a^{n} : = \left \{ {{a=0} if n is even \atop {a=1} if n is odd } \right.

this is a sequence where each number is repeated (n) times

the next three terms are 0 in 6 places, 1 in 7places and 0 in 9places

You might be interested in
Find k given that these three points are collinear.<br> A(0, -2), B(2, 0), and C(5, k)
goldfiish [28.3K]

Answer:

k = 3.

Step-by-step explanation:

If they are collinear the slope of AB = the slope of BC, so :-

(0- (-2)) / (2 - 0) = (k - 0) / (5 - 2)

2/2 = k/3

1 = k/3

k = 3.

7 0
3 years ago
If x2 = 40, what is the value of x?
Alina [70]
If you mean 2x=40 x=20 
but if you mean x^2=40 i think its x=80

8 0
3 years ago
Read 2 more answers
The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. The point (8, -2) is on the circle.
Jlenok [28]
From the equation, you can see that (3,-2) is the center of the circle (the terms are 0 for those x,y values). The mentioned point has the same y value as the center. That's good news, because it tells us that the tangent line is exactly vertical. The x coordinate is given as x=8. Vertical lines have an equation of x=... so x=8 is the right answer.
8 0
3 years ago
Read 2 more answers
Simplify (b^4)^3 A.B^9 B.B^3 C.B D.B^12
natulia [17]

(b^4)^3


To simplify when something is raised to two different exponents, multiply the two exponents together:

4 * 3 = 12

You now have b^12.


The answer is D.


6 0
3 years ago
2x+4y=16 what is the slope intercept form
Eva8 [605]
Since slope intercept is y=mx+b, you first want to get rid of the 2x by subtracting it from both sides. after, you should end up with 4y=16-2x or 4y=-2x+16, they both are the same, but some teachers might prefer the slope first. after that, you want to get the y alone, so you divide everything by 4. you should end up with the slope intercept form being y=-2/4x+4, simplified to y=-1/2x+4.
3 0
3 years ago
Other questions:
  • Larry Mary and Terry each had a full glass of juice Larry drank 3/4 of his Mary drank 3/8 of hers Terry drank 7/10 of his who dr
    9·1 answer
  • Which of the following is not approximately equivalent to one of the metric units: 1 kilometer, 1 meter, 1 kilogram, or 1 liter?
    8·1 answer
  • Please helpppp tyyy so much
    5·2 answers
  • Need help please please
    7·1 answer
  • Simplify the expression 10-4x(6+5-1) divided by 8+7
    15·1 answer
  • True or false? Postulates are statements that are accepted without question or justification
    5·2 answers
  • What is 8 time the square root of 6
    7·1 answer
  • A standard-size volleyball court has an area of 1,800 square feet. The length of the court is 60 feet. What is the width of the
    6·1 answer
  • Part A
    14·1 answer
  • What’s the missing side length of that question
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!