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Natalka [10]
3 years ago
15

A sequence can be described using the rule an = –2 + 3(n-1). Which is the

Mathematics
1 answer:
pishuonlain [190]3 years ago
6 0

Answer:The 20th term of the arithmetic sequence is 55

Step-by-step explanation:

A sequence can be described using the rule:

an = –2 + 3(n-1)

Where

an is the value of the nth term of the arithmetic sequence.

- 2 is the first term of term of the sequence.

n is the number of terms in the sequence.

To determine the 20th term, we will substitute n = 20 into the equation. It becomes

a20 = - 2 + 3(20 - 1)

a20 = - 2 + 3×19

a20 = -2 + 57 = 55

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Could I have some help on my patterns assignment​
nydimaria [60]

Answer:

1. 13, 18, 23, 28, 33, 38, 43, 48, 53

<em>Conjecture:</em> Each term is 5 more than the previous term.

2. 512, 256, 128, 64, 32, 16, 8, 4, 2

<em>Conjecture:</em> Each term is half of the previous term.

3. 1, 8, 27, 64, 125, 216, 343, 512, 729

<em>Conjecture:</em> Each term is a cube. To find the nth term, cube n.

4. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

<em>Conjecture:</em> Each term is the next consecutive prime number.

5. <u><em>Correct as is</em></u>

6. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

<em>Conjecture:</em> Each term is the sum of the 2 previous numbers.

Step-by-step explanation:

1.

Given: 13, 18, 23, 28

<em>We add 5 to each number</em>

13 + 5 = 18

18 + 5 = 23

23 + 5 = 28

28 + 5 = 33

33 + 5 = 38

38 + 5 = 43

43 + 5 = 48

48 + 5 = 53

2.

Given : 512, 256, 128, 64

<em>Divide each number by 2</em>

512 ÷ 2 =256

256 ÷ 2 = 128

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

3.

Given: 1, 8, 27, 64

<em>We have to cube n:</em>

<u><em>n³ = consecutive number cubed</em></u>

<u><em></em></u>

1³ = 1 or 1 × 1 × 1

2³ = 8 or 2 × 2 × 2

3³ = 27 or 3 × 3 × 3

4³ = 64 or 4 × 4 × 4

5³ = 125 or 5 × 5 × 5

6³ = 216 or 6 × 6 × 6

7³ = 343 or 7 × 7 × 7

8³ = 512 or 8 × 8 × 8

9³ = 729 or 9 × 9 × 9

4.

Consecutive prime number: <u><em>Consecutive prime numbers are those that have no gaps or prime numbers between them.</em></u>

Look at the picture in the link:

6.

Given: 1, 1, 2, 3, 5, 8

<em>We must add the two previous numbers to get the next term:</em>

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

21 = 34 = 55

34 + 55 = 89

8 0
1 year ago
Can you guys help me?
fiasKO [112]
16.
1/2= 0.5 and it takes 16 months to get to 8 inches.
0.5x16=8
8 0
3 years ago
Read 2 more answers
T.j. gave 16 books to the library book sale. this was 1/3 of his books. how many books did t.j. have?
madreJ [45]
(1/3)x =16 (x represents the total number of books he has)
x=48
8 0
3 years ago
Please help if you can and if you know how to help me understand these Im all ears.
maw [93]

Aight let's answer this step by step

What you need to know is if two values are equal either one will be similar to the other it's only the format that's different if you calculate each of the fractions you'll see each pair is equal except for the last option

Where if calculated

8/3=2.67 but

5/4.8=1.04

Therefore values aren't equal to each other

6 0
3 years ago
Read 2 more answers
A certain tennis player makes a successful first serve 6969​% of the time. Suppose the tennis player serves 9090 times in a matc
Wewaii [24]

Answer:

a) 4.387

b) Yes, because np & npq are greater than 10.

c) = 0.017          

Step-by-step explanation:

Give data:

p = 0.69

n = 90

a) a

E(X) = np = 62.1

SD(X) = \sqrt{(np(1-p))}

          =\sqrt{90\times 0.69(1- 0.69)}

          = 4.387

b)

np = 62.1  

q = 1 - p  = 1 - 0.69 = 0.31

npq = 19.251

Yes, because np & npq are greater than 10.

c.

P(X \geq 72   ) = P(X > 71.5) [continuity correction]

=    P(Z> \frac{((71.5-62.1)}{ 4.387})

= P(Z> 2.14 )      

= 1 - P(Z<2.14)              

= 1 - 0.983   (using table)          

= 0.017          

8 0
3 years ago
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