Help please Write the next three terms of the, №18010476, 10.03.2020 05:57

Mathematics

Help please Write the next three terms of the arithmetic sequence. 0.2, 0.6, 1, 0.4, __, __,__ Write the next three terms of the arithmetic sequence. 4, 3 3/4, 3 1/2, 3 1/4 ,__, __, __

Step-by-step answer

P Answered by Master

Use the formula for an arithmetic sequence: $a_{n}=a+(n-1)d$

$a_{n}$ = nth term

a = the first term in the sequence

n = term you are looking for

d = common difference between the terms

Answers

1. I'm assuming you meant to type 0.2, 0.6, 1, 1.4...

In that case, it is increasing by 0.4, so the next three would be:

0.2 + (4-1)(0.4) = 1.8...

=> 1.8, 2.2, 2.6.

2. Here it's reducing by 0.25, so start with:

4 + (5-1)(-0.25) = 3...

=> 3, 2.75, 2.5

Mathematics

2arithmetic sequences and series find the indicated term of each arithmetic sequence. 1. find the sixtieth term of the arithmetic sequence if a1 = 418 and d = 12. 2. find a23 in the sequence, –18, –34, –50, –66, write an equation for the nth term of each arithmetic sequence. 3. 45, 30, 15, 0, 4. –87, –73, –59, –45, find the sum of each arithmetic series. 5. 5 + 7 + 9 + 11 + + 27 6. –4 + 1 + 6 + 11 + + 91 7. 13 + 20 + 27 + + 272 8. 89 + 86 + 83 + 80 + + 20 9. ∑ (1 − 2n) 4 n=1 10. ∑ (5 + 3j) 6 j=1 11. ∑ (9 − 4n) 5 n=1 12. ∑ (2k + 1) 10 k=4 13. ∑

Step-by-step answer

P Answered by Specialist

8

I have the first 8 answers for you:
1: 1126
2: -370
3: a_n=45-15(n-1)

4:

5: 192
6: 870
7: 5414
8: 1308

The formula for #1 would be a_n=418+12(n-1)

. Using 60 for n, we have
418+12(60-1) = 1126

The formula for #2 would be a_n=-18-16(n-1)

. Using 23 for n, we have
-18-16(23-1) = -370

The general form for this sequence is a_n=a_1+d(n-1)

, where a₁ is the first term and d is the common difference. For #3, the first term is 45 and the common difference is -15. For #4, the first term is -87 and the common difference is 14.

For #5-8, add together the terms.

Mathematics

2arithmetic sequences and series find the indicated term of each arithmetic sequence. 1. find the sixtieth term of the arithmetic sequence if a1 = 418 and d = 12. 2. find a23 in the sequence, –18, –34, –50, –66, write an equation for the nth term of each arithmetic sequence. 3. 45, 30, 15, 0, 4. –87, –73, –59, –45, find the sum of each arithmetic series. 5. 5 + 7 + 9 + 11 + + 27 6. –4 + 1 + 6 + 11 + + 91 7. 13 + 20 + 27 + + 272 8. 89 + 86 + 83 + 80 + + 20 9. ∑ (1 − 2n) 4 n=1 10. ∑ (5 + 3j) 6 j=1 11. ∑ (9 − 4n) 5 n=1 12. ∑ (2k + 1) 10 k=4 13. ∑

Step-by-step answer

P Answered by Master

8

I have the first 8 answers for you:
1: 1126
2: -370
3: a_n=45-15(n-1)

4:

5: 192
6: 870
7: 5414
8: 1308

The formula for #1 would be a_n=418+12(n-1)

. Using 60 for n, we have
418+12(60-1) = 1126

The formula for #2 would be a_n=-18-16(n-1)

. Using 23 for n, we have
-18-16(23-1) = -370

The general form for this sequence is a_n=a_1+d(n-1)

, where a₁ is the first term and d is the common difference. For #3, the first term is 45 and the common difference is -15. For #4, the first term is -87 and the common difference is 14.

For #5-8, add together the terms.

Mathematics

J. 26 ply answering the following qu Learning Task 1. Write the letter before the number. The letters will spell out the Khmer greeting. 1. What is the 5th term of the arithmetic sequence an= 5n + 1 ? G. 23 H. 24 I. 25 2. What is the next 3 terms of the Fibonacci sequence 0, 1, 1, 2, 3, 5,...? T. 8, 10, 18 U. 8, 13, 21 V. 8, 12, 16 W. 8, 11, 14 3. What are the missing numbers in the sequence 4, ---,_,_, 64 ? M. 8, 16, 32 N. 8, 14, 28 0.8, 18, 28 P. 8, 12, 16 4. What is the common ratio of the given sequence 3, -6, 12,-24, 48 ? Q.-2 R. 2 S. 3 T.

Step-by-step answer

P Answered by PhD

1

See explanation

Step-by-step explanation:

1. What is the 5th term of the arithmetic sequence an= 5n + 1 ?

This will be:

= 5n + 1

= 5(5) + 1

= 25 + 1

= 26

2. What is the next 3 terms of the Fibonacci sequence 0, 1, 1, 2, 3, 5,

Fibonacci sequence means that you'll add the two previous numbers given to get the next number. Therefore, the next numbers will be:

3+5 = 8

5+8 = 13

8 + 13 = 21

The numbers are 8, 13 and 21.

3. What are the missing numbers in the sequence 4, ---,_,_, 64 ?

a = 4

ar^4 = 64

We replace a with 4

4r^4 = 64

r^4 = 64/4

r^4 = 16

r = 2

2nd term = ar = 4 × 2 = 8

3rd term = ar^2 = 4 × 2^2 = 4 × 4 = 16

4th term = ar^3 = 4 × 2^3 = 4 ×✓8 = 32

The numbers are 8, 16 and 32.

4. What is the common ratio of the given sequence 3, -6, 12,-24, 48 ?

Common ratio = 2nd term / 1st term

= ar / a

= -6/3

= -2

5. What is the 10th term of the arithmetic sequence an = 3n - 5 ?

an = 3n - 5

= 3(10) - 5

= 30 - 5

= 25

6. If a1 = 2, d = -2, then what is a 12?

a12 = a + (n - 1)d

a12 = a + (12 - 1)d

a12 = a + 11d

a12 = 2 + 11(-2)

a12 = 2 - 22

a12 = -20

7. What is the common ratio of the given sequence 1000, 500, 250, 125?

Common ratio = 2nd term / 1st term

= 500 / 1000

= 1/2

8. What is the 8th term of the sequence -10, - 8, -6, -4, ...?

a = -10

d = -8 - (-10) = -8 + 10 = 2

8th term = a + (n - 1)d

= a + (8 - 1)d

= a + 7d

= -10 + 7(2)

= -10 + 14

= 4

9. What is the Khmer greetings?

It is a greeting used by Cambodians when they meet and they will say Choum Reap Sur which simply means Hello. Also, when they're leaving they'll Som Pas and then the person will say Choum Reap Lir which mean Goodbye. It should be noted that Don Pas is used by Cambodians to greet and to also show respect for someone.

Mathematics

J. 26 ply answering the following qu Learning Task 1. Write the letter before the number. The letters will spell out the Khmer greeting. 1. What is the 5th term of the arithmetic sequence an= 5n + 1 ? G. 23 H. 24 I. 25 2. What is the next 3 terms of the Fibonacci sequence 0, 1, 1, 2, 3, 5,...? T. 8, 10, 18 U. 8, 13, 21 V. 8, 12, 16 W. 8, 11, 14 3. What are the missing numbers in the sequence 4, ---,_,_, 64 ? M. 8, 16, 32 N. 8, 14, 28 0.8, 18, 28 P. 8, 12, 16 4. What is the common ratio of the given sequence 3, -6, 12,-24, 48 ? Q.-2 R. 2 S. 3 T.

Step-by-step answer

P Answered by PhD

1

See explanation

Step-by-step explanation:

1. What is the 5th term of the arithmetic sequence an= 5n + 1 ?

This will be:

= 5n + 1

= 5(5) + 1

= 25 + 1

= 26

2. What is the next 3 terms of the Fibonacci sequence 0, 1, 1, 2, 3, 5,

Fibonacci sequence means that you'll add the two previous numbers given to get the next number. Therefore, the next numbers will be:

3+5 = 8

5+8 = 13

8 + 13 = 21

The numbers are 8, 13 and 21.

3. What are the missing numbers in the sequence 4, ---,_,_, 64 ?

a = 4

ar^4 = 64

We replace a with 4

4r^4 = 64

r^4 = 64/4

r^4 = 16

r = 2

2nd term = ar = 4 × 2 = 8

3rd term = ar^2 = 4 × 2^2 = 4 × 4 = 16

4th term = ar^3 = 4 × 2^3 = 4 ×✓8 = 32

The numbers are 8, 16 and 32.

4. What is the common ratio of the given sequence 3, -6, 12,-24, 48 ?

Common ratio = 2nd term / 1st term

= ar / a

= -6/3

= -2

5. What is the 10th term of the arithmetic sequence an = 3n - 5 ?

an = 3n - 5

= 3(10) - 5

= 30 - 5

= 25

6. If a1 = 2, d = -2, then what is a 12?

a12 = a + (n - 1)d

a12 = a + (12 - 1)d

a12 = a + 11d

a12 = 2 + 11(-2)

a12 = 2 - 22

a12 = -20

7. What is the common ratio of the given sequence 1000, 500, 250, 125?

Common ratio = 2nd term / 1st term

= 500 / 1000

= 1/2

8. What is the 8th term of the sequence -10, - 8, -6, -4, ...?

a = -10

d = -8 - (-10) = -8 + 10 = 2

8th term = a + (n - 1)d

= a + (8 - 1)d

= a + 7d

= -10 + 7(2)

= -10 + 14

= 4

9. What is the Khmer greetings?

It is a greeting used by Cambodians when they meet and they will say Choum Reap Sur which simply means Hello. Also, when they're leaving they'll Som Pas and then the person will say Choum Reap Lir which mean Goodbye. It should be noted that Don Pas is used by Cambodians to greet and to also show respect for someone.

Mathematics

Describe the relationship between the terms in each arithmetic sequence. Then write the next three terms in the sequence. 0.4, 0.8, 1.2, 1.6, ...

Step-by-step answer

P Answered by PhD

2

Please check the explanation.

Step-by-step explanation:

Given the sequence

0.4, 0.8, 1.2, 1.6, ...

An Arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$