1. Find the next two terms of the sequence.
2, 6, 10, 14, ellipsis (1 point)
16, 18
18, 24
18, 22
16, 20
2. Find the next two terms of the sequence.
10, 4, negative 2, negative 8, ellipsis (1 point)
negative 6, negative 10
negative 10, negative 12
negative 12, negative 16
negative 14, negative 20
3. Find the next two terms of the sequence.
2, 20, 200, 2000, ellipsis (1 point)
20,000, 200,000
20,000, 2,000,000
4, 40
200,000, 2,000,000
4. Find the next two terms of the sequence.
1.1, 2.2, 3.3, 4.4, ellipsis (1 point)
4.5, 5.5
5, 6
5.6, 6.7
5.5, 6.6
5. Tell whether the sequence is arithmetic. If it is, identify the common difference.
negative 7, negative 3, 1, 5, ellipsis (1 point)
Not arithmetic
Arithmetic, common difference is 4
Arithmetic, common difference is 8
Arithmetic, common difference is 7
6. Tell whether the sequence is arithmetic. If it is, identify the common difference.
negative 9, negative 17, negative 26, negative 33, ellipsis (1 point)
Not arithmetic
Arithmetic, common difference is 8
Arithmetic, common difference is 9
Arithmetic, common difference is 7
7. Tell whether the sequence is arithmetic. If it is, identify the common difference.
nineteen eight negative three negative fourteen elipsis (1 point)
Not arithmetic
Arithmetic, common difference is negative 11
Arithmetic, common difference is 5
Arithmetic, common difference is 17
8. Tell whether the sequence is arithmetic. If it is, identify the common difference.
one-half, one-third, one-fourth, ellipsis (1 point)
Not arithmetic
Arithmetic, common difference is one-sixth
Arithmetic, common difference is two-thirds
Arithmetic, common difference is 1
9. Write a function rule to represent the sequence.
0.3, 0.9, 1.5, 2.1, ellipsis (1 point)
A of n equals 0.6 plus left parenthesis n minus 1 right parenthesis times 0.3
A of n equals 0.6 minus left parenthesis n right parenthesis times 0.3.
A of n equals 0.3 plus left parenthesis n minus 1 right parenthesis times 0.6
A of n equals 0.3 plus left parenthesis n plus 1 right parenthesis times 0.6
10. Write a function rule to represent the sequence.
47, 32, 17, 2, ellipsis (1 point)
A of n equals 47 plus left parenthesis n minus 1 right parenthesis times 15
A of n equals 47 plus left parenthesis n minus 1 right parenthesis times negative 13
A of n equals 47 plus left parenthesis n minus 1 right parenthesis times negative 15
A of n equals 32 plus left parenthesis n minus 1 right parenthesis times 15
Practice: Arithmetic Sequences Practice
1. C
2. D
3. A
4. D
5. B
6. A
7. B
8. A
9. C
10.C
*All correct answers*
#1, keep adding 4
These are all very similar.
Just subtract the first term from the second to get the amount you have to keep adding.
For the ones you have to check, as whether the same amount is added each time. If not, it's not an Arithmetic Sequence.
subtract the first term from the second to see what you need to keep adding.
For #1, that would be 4.
Similarly for all the rest
Yes,
I agree. If you do this it will help you figure out the answers on your own without cheating.
1. 18, 22
2. Negative 12, negative 16
3. 20,000, 2,000,000
4. 5.5, 6.6
5. Arithmetic, common difference is 4
6. Arithmetic, common difference is 9
7. Not arithmetic
8. Not arithmetic
9. A of n equals 0.3 plus (n-1) times 0.6
10. A of n equals 47 plus (n-1) times -15
1. To find the next two terms of the sequence 2, 6, 10, 14, ... , we can observe that each term increases by 4. So, to find the next term, we add 4 to the last term. The last term is 14, so the next term is 14 + 4 = 18. Continuing with the same pattern, the term after 18 would be 18 + 4 = 22. Therefore, the next two terms of the sequence are 18 and 22.
2. Similarly, for the sequence 10, 4, -2, -8, ... , we can observe that each term decreases by 6. So, to find the next term, we subtract 6 from the last term. The last term is -8, so the next term is -8 - 6 = -14. Continuing with the same pattern, the term after -14 would be -14 - 6 = -20. Therefore, the next two terms of the sequence are -14 and -20.
3. For the sequence 2, 20, 200, 2000, ... , we can observe that each term is obtained by multiplying the previous term by 10. So, to find the next term, we multiply the last term by 10. The last term is 2000, so the next term is 2000 * 10 = 20,000. Continuing with the same pattern, the term after 20,000 would be 20,000 * 10 = 200,000. Therefore, the next two terms of the sequence are 20,000 and 200,000.
4. The sequence 1.1, 2.2, 3.3, 4.4, ... , is an arithmetic sequence with a common difference of 1. To find the next term, we add 1 to the last term. The last term is 4.4, so the next term is 4.4 + 1 = 5.4. Continuing with the same pattern, the term after 5.4 would be 5.4 + 1 = 6.4. Therefore, the next two terms of the sequence are 5.4 and 6.4.
5. The sequence -7, -3, 1, 5, ... , is an arithmetic sequence with a common difference of 4. The difference between each term is always 4. Therefore, the sequence is arithmetic, and the common difference is 4.
6. The sequence -9, -17, -26, -33, ... , is not an arithmetic sequence because the difference between each term is not constant. Therefore, the sequence is not arithmetic.
7. The sequence nineteen, eight, negative three, negative fourteen, ... , is not an arithmetic sequence because the difference between each term is not constant. Therefore, the sequence is not arithmetic.
8. The sequence one-half, one-third, one-fourth, ... , is not an arithmetic sequence because the difference between each term is not constant. Therefore, the sequence is not arithmetic.
9. To write a function rule to represent the sequence 0.3, 0.9, 1.5, 2.1, ... , we can observe that each term is obtained by adding 0.6 to the previous term. So, the function rule would be A(n) = 0.6 + (n - 1) * 0.3. This means that to find the nth term, we substitute n into the function: A(1) = 0.6, A(2) = 0.9, A(3) = 1.5, A(4) = 2.1, and so on.
10. To write a function rule to represent the sequence 47, 32, 17, 2, ... , we can observe that each term is obtained by subtracting 15 from the previous term. So, the function rule would be A(n) = 47 + (n - 1) * -15. This means that to find the nth term, we substitute n into the function: A(1) = 47, A(2) = 32, A(3) = 17, A(4) = 2, and so on.