# 9114 Number Patterns Arithmetic Rule From First 3 Terms

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| By Anthony Nunan
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Anthony Nunan
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Quizzes Created: 136 | Total Attempts: 44,016
Questions: 20 | Attempts: 154

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In this quiz, we are given the first three terms, and have to create the rule from those terms.
So. . . From 3, 205, 405, the answer becomes : tn=-195+200n
In this quiz, you are given and you only need to type out the right side of the equation.

• 1.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given rule for the arithmetic sequence is -25-8n. This means that each term in the sequence can be obtained by subtracting 8 multiplied by the position of the term (n) from -25. This rule follows the pattern of decreasing by 8 as n increases, resulting in a sequence of numbers that get progressively smaller.

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• 2.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given arithmetic sequence is 17+6n, where n represents the position of the term in the sequence. This means that the first term is 17, the second term is 17+6(1) = 23, the third term is 17+6(2) = 29, and so on. The pattern is that each term is obtained by adding 6 to the previous term. Therefore, the correct answer is 17+6n.

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• 3.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given sequence follows an arithmetic pattern where each term is obtained by subtracting 3n from 1. This means that for each term, the value of n increases by 1 and is multiplied by -3, which is then subtracted from 1. Therefore, the correct answer is 1-3n.

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• 4.

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• 6.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given rule for the arithmetic sequence is -48+10n. This means that each term in the sequence can be found by multiplying the position of the term (n) by 10 and then subtracting 48. For example, when n=1, the first term is -48+10(1) = -38. When n=2, the second term is -48+10(2) = -28. This pattern continues for each term in the sequence.

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• 7.

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• 9.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given arithmetic sequence can be represented by the formula 36-30n, where n represents the position of each term in the sequence. This means that as n increases, the terms in the sequence decrease by 30. For example, when n=1, the first term is 36-30(1) = 6, and when n=2, the second term is 36-30(2) = -24. Therefore, the formula accurately describes the pattern in the sequence.

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• 10.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given rule for the arithmetic sequence is -136+100n. This means that each term in the sequence is obtained by multiplying the position of the term (n) by 100 and then subtracting 136 from it. This rule will give us the correct value for each term in the sequence.

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• 11.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given arithmetic sequence is represented by the formula -19+8n, where n represents the position of each 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. For example, when n=1, the first term is -19+8(1) = -11. Similarly, when n=2, the second term is -19+8(2) = -3. Therefore, the formula -19+8n correctly represents the arithmetic sequence.

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• 12.

• 13.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given sequence follows the rule of an arithmetic sequence, where each term is obtained by adding a constant difference of 30 to the previous term. The term is represented by the formula -29+30n, where n represents the position of the term in the sequence.

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• 14.

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• 17.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given rule for the arithmetic sequence is -21+3n, where n represents the position of the term in the sequence. This means that to find any term in the sequence, we can substitute the value of n into the formula. The term will then be equal to -21 plus 3 times the position of the term in the sequence. This formula allows us to easily determine the value of any term in the sequence without having to calculate each term individually.

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• 18.

### For the sequence above, the rule for the arithmetic sequence is :

Explanation
The given rule for the arithmetic sequence is -27-4n. This means that each term in the sequence can be obtained by subtracting 4n from -27, where n represents the position of the term in the sequence. For example, when n is 1, the first term is -27-4(1) = -31. When n is 2, the second term is -27-4(2) = -35. This pattern continues for each term in the sequence.

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• 19.

• 20.