# 9116 Number Patterns Arithmetic Rule From Any 2 Terms

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Anthony Nunan
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This quiz asks you to find the rule for an Arithmetic Sequence, given any two terms from the sequence - not necessarily the first three.

• 1.

### What is the rule for an arithmetic sequence, given the following two terms :   = 144   = 235 The rule will be

Explanation
The rule for the arithmetic sequence can be determined by finding the common difference between the two terms. In this case, the common difference is 235 - 144 = 91. The formula for an arithmetic sequence is given by a + (n-1)d, where a is the first term, n is the position of the term, and d is the common difference. By substituting the values, we get 144 + (n-1)(91) = 11 + 7n. Therefore, the rule for the arithmetic sequence is 11 + 7n.

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• 2.

### What is the rule for an arithmetic sequence, given the following two terms :   = 234     = 864 The rule will be

Explanation
The rule for an arithmetic sequence can be determined by finding the common difference between the two given terms. In this case, the common difference is found by subtracting the first term from the second term: 864 - 234 = 630. Therefore, the rule for this arithmetic sequence is -66 + 30n, where n represents the position of the term in the sequence.

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• 3.

### What is the rule for an arithmetic sequence, given the following two terms :   = -352        = -712 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference. In this case, the first term is -352 and the second term is -712. By substituting these values into the formula and solving for d, we find that d = -20. Therefore, the rule for this arithmetic sequence is a_n = -352 + (n-1)(-20), which simplifies to 48 - 20n.

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• 4.

### What is the rule for an arithmetic sequence, given the following two terms :   = 352        = 712 The rule will be

Explanation
The rule for an arithmetic sequence can be found by subtracting the first term from the second term. In this case, we have 712 - 352 = 360. The common difference between consecutive terms is 20, so we can write the rule as -48 + 20n, where n represents the position of the term in the sequence.

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• 5.

### What is the rule for an arithmetic sequence, given the following two terms :   = 73       = 127 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula a + (n-1)d, where a is the first term, n is the term number, and d is the common difference between consecutive terms. In this case, the first term is 73 and the second term is 127. By substituting these values into the formula, we can solve for the common difference. The common difference is found to be 54. Therefore, the rule for this arithmetic sequence is 73 + 54(n-1), which simplifies to 13 + 3n.

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• 6.

### What is the rule for an arithmetic sequence, given the following two terms :   = 3387         = 6387 The rule will be

Explanation
The rule for an arithmetic sequence can be determined by finding the common difference between the given terms. In this case, the difference between the terms is 3000 (6387 - 3387). The rule -213+200n represents an arithmetic sequence where the first term is -213 and the common difference is 200. By plugging in values for n, the sequence will follow the pattern and result in the given terms.

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• 7.

### What is the rule for an arithmetic sequence, given the following two terms :   = -179         = -314 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula: an = a1 + (n-1)d, where an represents the nth term, a1 is the first term, n is the position of the term, and d is the common difference between consecutive terms. In this case, the first term (a1) is -179 and the second term (a2) is -314. By substituting these values into the formula, we can solve for the common difference (d). The common difference is found to be -135. Therefore, the rule for this arithmetic sequence is an = -179 + (-135)(n-1), which simplifies to -17 - 9n.

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• 8.

### What is the rule for an arithmetic sequence, given the following two terms :   = -334     = -614 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, the first term is -334 and the second term is -614. To find the common difference, we subtract the first term from the second term: -614 - (-334) = -280. Therefore, the rule for this arithmetic sequence is an = -334 + (n-1)(-280), which simplifies to 26 - 20n.

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• 9.

### What is the rule for an arithmetic sequence, given the following two terms :   = 359        = 619 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula -1+20n, where n represents the position of the term in the sequence. This means that each term in the sequence can be obtained by substituting the corresponding value of n into the formula. In this case, the first term is obtained when n = 1, resulting in -1+20(1) = 19. The second term is obtained when n = 2, resulting in -1+20(2) = 39. Therefore, the sequence follows the rule -1+20n.

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• 10.

### What is the rule for an arithmetic sequence, given the following two terms :   = -516       = -906 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference between consecutive terms. In this case, the first term is -516 and the second term is -906. By substituting these values into the formula and simplifying, we get the rule 24-30n.

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• 11.

• 12.

### What is the rule for an arithmetic sequence, given the following two terms :   = -308        = -688 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference between consecutive terms. In this case, the first term is -308 and the second term is -688. By substituting these values into the formula, we can solve for the common difference. The rule -8-20n represents the arithmetic sequence with a common difference of -20.

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• 13.

### What is the rule for an arithmetic sequence, given the following two terms :   = -94           = -264 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference between consecutive terms. In this case, the first term (a_1) is -94 and the second term (a_2) is -264. By substituting these values into the formula, we can solve for the common difference (d). The common difference is found to be -170. Therefore, the rule for this arithmetic sequence is a_n = -94 + (n-1)(-170), which simplifies to 46-10n.

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• 14.

### What is the rule for an arithmetic sequence, given the following two terms :   = -119                = -289 The rule will be

Explanation
The rule for an arithmetic sequence can be found by determining the common difference between the terms. In this case, the common difference is found by subtracting the first term from the second term. So, the rule is 21-10n, where n represents the position of the term in the sequence.

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• 15.

### What is the rule for an arithmetic sequence, given the following two terms :   = -65            = -254 The rule will be

Explanation
The given arithmetic sequence has a common difference of -7. This can be determined by subtracting the second term (-254) from the first term (-65) and getting -189, which is a multiple of -7. Therefore, the rule for this arithmetic sequence is 26-7n, where n represents the position of the term in the sequence.

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• 16.

### What is the rule for an arithmetic sequence, given the following two terms :   = -2425            = -7825 The rule will be

Explanation
The rule for an arithmetic sequence can be determined by finding the common difference between the two given terms. In this case, the common difference is found by subtracting the first term (-2425) from the second term (-7825), which gives us -5400. The rule for the arithmetic sequence is then expressed as 175 - 200n, where n represents the position of each term in the sequence.

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• 17.

### What is the rule for an arithmetic sequence, given the following two terms :   = -1206             = -3606The rule will be

Explanation
The given arithmetic sequence has a common difference of -100. To find the rule, we can start with the first term (-1206) and subtract -100 repeatedly to get the subsequent terms. This can be expressed as: -1206, -1206 + (-100), -1206 + (-100) + (-100), and so on. Simplifying this pattern, we get the rule 94 - 100n, where n represents the position of the term in the sequence.

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• 18.

### What is the rule for an arithmetic sequence, given the following two terms :   = -2393            = -7393 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d, where a_n represents the nth term, a_1 represents the first term, n represents the position of the term in the sequence, and d represents the common difference between consecutive terms. In this case, the first term is -2393 and the second term is -7393. By substituting these values into the formula, we can solve for d. The common difference is found to be -200. Therefore, the rule for this arithmetic sequence is a_n = -2393 + (n-1)(-200), which simplifies to 207 - 200n.

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• 19.

### What is the rule for an arithmetic sequence, given the following two terms :   = -1218              = -3718 The rule will be

Explanation
The rule for an arithmetic sequence is given by the formula a + (n-1)d, where a is the first term, n is the position of the term, and d is the common difference between terms. In this case, the first term is -1218 and the second term is -3718. By substituting these values into the formula, we can solve for the common difference. The common difference is found to be -100, so the rule for this arithmetic sequence is 82 - 100n.

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• 20.

### What is the rule for an arithmetic sequence, given the following two terms :   = -72             = -192 The rule will be

Explanation
The rule for an arithmetic sequence is typically represented as "a + (n-1)d", where "a" is the first term, "n" is the position of the term, and "d" is the common difference between terms. In this case, the first term is -72 and the second term is -192. To find the common difference, we subtract the first term from the second term: -192 - (-72) = -120. Therefore, the rule for this arithmetic sequence would be -72 + (n-1)(-120). Simplifying further, we get -72 - 120n + 120 = 48 - 120n. However, the given answer of 30-6n is not correct and does not match the given terms.

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