1.
When a = 30, and d = 100
The rule for the Arithmetic Sequence is
Explanation
The given rule for the arithmetic sequence is -70 + 100n. This means that each term in the sequence is found by subtracting 70 from 100 times the position of the term (n). So, when a = 30 and d = 100, we can plug these values into the rule to find the answer. Plugging in a = 30, we get -70 + 100n = 30. Solving for n, we find that n = 1. Therefore, the answer is -70 + 100(1) = 30.
2.
When a = 15 , and d = -4
The rule for the Arithmetic Sequence is
3.
When a = 1, and d = 4
The rule for the Arithmetic Sequence is
Explanation
The given rule for the Arithmetic Sequence is -3+4n. This means that each term in the sequence is obtained by adding 4 times the position of the term (n) to -3. For example, when n is 1, the term is -3+4(1) = 1. When n is 2, the term is -3+4(2) = 5. This pattern continues for all values of n, resulting in an arithmetic sequence.
4.
When a = 25, and d = 6
The rule for the Arithmetic Sequence is
5.
When a = 38, and d = 10
The rule for the Arithmetic Sequence is
Explanation
The given formula for the arithmetic sequence is 28 + 10n, where n represents the position of the term in the sequence. This means that each term in the sequence can be found by adding 10 to the previous term. For example, when n = 1, the first term is 28 + 10(1) = 38. When n = 2, the second term is 28 + 10(2) = 48. And so on. Therefore, the correct answer is 28 + 10n.
6.
When a = 6, and d = 10
The rule for the Arithmetic Sequence is
Explanation
The given answer, -4+10n, represents the formula for finding the nth term of an arithmetic sequence. In this case, the common difference (d) is 10, meaning that each term increases by 10. The first term (a) is 6. By substituting these values into the formula, we can find the value of any term in the sequence.
7.
When a = 7, and d = 10
The rule for the Arithmetic Sequence is
Explanation
The given answer, -3+10n, represents the formula for finding the nth term of an arithmetic sequence when a = 7 and d = 10. In this formula, -3 represents the initial term (a) of the sequence, and 10 represents the common difference (d) between each term. The variable n represents the position of the term in the sequence. By substituting the given values of a and d into the formula, we can find the value of any term in the sequence.
8.
When a = 23, and d = -100
The rule for the Arithmetic Sequence is
9.
When a = 8, and d = -100
The rule for the Arithmetic Sequence is
10.
When a = 18, and d = -9
The rule for the Arithmetic Sequence is
11.
When a = 11, and d = -3
The rule for the Arithmetic Sequence is
Explanation
The rule for the Arithmetic Sequence is given by 14-3n, where n represents the position of the term in the sequence. In this case, when a = 11 and d = -3, the value of n is not provided. Therefore, the answer 14-3n is a general formula that represents the terms of the Arithmetic Sequence for any value of n.
12.
When a = 35, and d = -5
The rule for the Arithmetic Sequence is
13.
When a = -9, and d = -2
The rule for the Arithmetic Sequence is
14.
When a = -2, and d = -8
The rule for the Arithmetic Sequence is
Explanation
The given answer, 6-8n, is the formula for the arithmetic sequence when a = -2 and d = -8. In an arithmetic sequence, the value of each term can be found by adding a constant difference, d, to the previous term. Here, the constant difference is -8, meaning that each term is 8 less than the previous term. The first term, a, is -2. Therefore, the formula for the arithmetic sequence is 6-8n, where n represents the position of the term in the sequence.
15.
When a = -38, and d = 200
The rule for the Arithmetic Sequence is
Explanation
The given answer, -238+200n, represents the rule for the arithmetic sequence when a = -38 and d = 200. In an arithmetic sequence, the first term (a) is -38 and the common difference (d) is 200. The formula for finding the nth term of an arithmetic sequence is a + (n-1)d. By substituting the given values into the formula, we get -38 + (n-1)200, which simplifies to -238 + 200n. Therefore, the given answer is correct.
16.
When a = -24, and d = -5
The rule for the Arithmetic Sequence is
Explanation
The given rule for the arithmetic sequence is -19-5n. This means that each term in the sequence can be found by subtracting 5 times the position of the term (n) from -19. For example, when n=1, the first term is -19-5(1) = -24. When n=2, the second term is -19-5(2) = -29. This pattern continues for all values of n in the sequence.
17.
When a = -36, and d = -10
The rule for the Arithmetic Sequence is
18.
When a = -19, and d = -20
The rule for the Arithmetic Sequence is
19.
When a = -26, and d = -6
The rule for the Arithmetic Sequence is
Explanation
The given answer, -20-6n, represents the formula for an arithmetic sequence. In this formula, -20 is the initial term (a) and -6 is the common difference (d). The variable n represents the position of the term in the sequence. By plugging in the values of a = -26 and d = -6, we can use this formula to find the specific terms in the arithmetic sequence.
20.
When a = -14, and d = 9
The rule for the Arithmetic Sequence is
Explanation
The given rule for the arithmetic sequence is -23+9n, where n represents the position of the term in the sequence. This means that each term in the sequence can be found by substituting the value of n into the formula. In this case, when a = -14, we need to find the corresponding value of n. By substituting -14 into the formula and solving for n, we can determine the position of the term.
21.
When a = -7, and d = 7
The rule for the Arithmetic Sequence is
Explanation
The rule for the arithmetic sequence is given by -14+7n, where 'n' represents the position of the term in the sequence. When a = -7 and d = 7, we can substitute these values into the formula to find the nth term. The formula simplifies to -14+7n, which represents the arithmetic sequence with a common difference of 7 and starting term of -14.
22.
When a = -31, and d = 9
The rule for the Arithmetic Sequence is
Explanation
The given answer, -40+9n, represents the rule for an arithmetic sequence. In an arithmetic sequence, each term is obtained by adding a constant difference, d, to the previous term. In this case, the first term is -40 and the common difference is 9. By multiplying the common difference, 9, with the variable n (which represents the position of the term in the sequence), we can find the value of each term in the sequence.
23.
When a = -11, and d = 200
The rule for the Arithmetic Sequence is
Explanation
The given answer, -211+200n, represents the general formula for the arithmetic sequence when a = -11 and d = 200. In an arithmetic sequence, the first term (a) is -11 and the common difference (d) is 200. The formula -211+200n allows us to find any term in the sequence by substituting the value of n, which represents the position of the term. By plugging in different values for n, we can calculate the corresponding terms in the sequence.
24.
When a = -4, and d = 7
The rule for the Arithmetic Sequence is
Explanation
The given rule for the arithmetic sequence is -11+7n, where n represents the position of the term in the sequence. When a = -4 and d = 7, we can substitute these values into the rule to find the specific term in the sequence. By plugging in -4 for a and 7 for d, we get -11+7n. This represents the general term of the arithmetic sequence when a = -4 and d = 7.
25.
When a = -29, and d = 5
The rule for the Arithmetic Sequence is
Explanation
The given rule for the Arithmetic Sequence is -34+5n. This means that each term in the sequence can be obtained by adding 5 times the position of the term (represented by n) to -34. For example, when n=1, the first term is -34+5(1) = -29. Similarly, when n=2, the second term is -34+5(2) = -24. This pattern continues for each term in the sequence.
26.
When a = -21, and d = 2
The rule for the Arithmetic Sequence is
Explanation
The given answer, -23+2n, represents the formula for finding the nth term of an arithmetic sequence. In this formula, -23 is the first term of the sequence and 2 is the common difference between each term. By substituting the values of a = -21 and d = 2 into the formula, we can find any term in the sequence by replacing n with the desired term number.
27.
When a = -33, and d = 10The rule for the Arithmetic Sequence is
Explanation
The given rule for the arithmetic sequence is -43+10n, where n represents the position in the sequence. When a = -33 and d = 10, we can substitute these values into the rule. By substituting n = 1, we get -43 + 10(1) = -33, which matches the given value of a. Therefore, the given rule is correct for this arithmetic sequence.
28.
When a = -14, and d = 9
The rule for the Arithmetic Sequence is
Explanation
The given arithmetic sequence has a common difference of 9. To find the nth term of the sequence, we can use the formula -23 + 9n, where n represents the position of the term in the sequence. By substituting the value of a as -23 and d as 9, we can find any term in the sequence by plugging in the value of n.
29.
When a = -36, and d = 20
The rule for the Arithmetic Sequence is
Explanation
The given arithmetic sequence has a common difference of 20 and starts with the term -56. To find any term in the sequence, we can use the formula -56 + 20n, where n represents the position of the term in the sequence. By substituting the given values a = -36 and d = 20 into the formula, we can find the term at any specific position.
30.
When a = -16, and d = 20
The rule for the Arithmetic Sequence is
Explanation
The given answer, -36+20n, represents the formula for finding the nth term of an arithmetic sequence when the first term is -36 and the common difference is 20. By substituting the value of n, we can find any term in the sequence.
31.
When a = -26, and d = 20
The rule for the Arithmetic Sequence is
Explanation
The given answer, -46+20n, represents the rule for the arithmetic sequence when a = -26 and d = 20. In an arithmetic sequence, each term is found by adding a constant difference, d, to the previous term. Here, the first term, a, is -26 and the common difference, d, is 20. By substituting these values into the formula -46+20n, we can find any term in the sequence by plugging in the value of n.
32.
When a = 16, and d = 18The rule for the Arithmetic Sequence is
Explanation
The given answer, -2+18n, represents the formula for finding the nth term of an arithmetic sequence when the common difference (d) is 18 and the first term (a) is -2. In this formula, n represents the position of the term in the sequence. By substituting different values of n, we can find the corresponding terms in the sequence. For example, when n=1, the first term in the sequence is -2, and when n=2, the second term is 16. This formula allows us to easily calculate any term in the arithmetic sequence.
33.
When a = 28, and d = 30
The rule for the Arithmetic Sequence is
Explanation
The given answer -2+30n represents the formula for finding the nth term of an arithmetic sequence when the first term is -2 and the common difference is 30. By substituting the value of n with any positive integer, we can find the corresponding term in the sequence. For example, when n=1, the first term of the sequence is -2+30(1) = 28. Similarly, when n=2, the second term is -2+30(2) = 58. This formula allows us to calculate any term in the sequence by plugging in the value of n.
34.
When a = 3, and d = 200
The rule for the Arithmetic Sequence is
Explanation
The given answer, -197+200n, represents the rule for the arithmetic sequence when a=3 and d=200. In an arithmetic sequence, each term is found by adding a constant difference, d, to the previous term. Here, the first term is 3, and the common difference is 200. By substituting the values into the formula, we get -197+200n, which gives us the nth term of the arithmetic sequence.
35.
When a = 31, and d = 200
The rule for the Arithmetic Sequence is
Explanation
The given answer, -169+200n, represents the formula for finding the nth term of an arithmetic sequence when the first term is -169 and the common difference is 200. In this formula, n represents the position of the term in the sequence. By substituting different values for n, we can find the corresponding terms in the sequence.
36.
When a = 26, and d = 5
The rule for the Arithmetic Sequence is
Explanation
The given rule for the Arithmetic Sequence is 21+5n, where n represents the position of the term in the sequence. This means that to find any term in the sequence, we need to multiply the position of the term by 5 and add 21 to it.