consecutive integers

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What are consecutive integers?

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Consecutive integers are integers that follow each other in order, without any gaps. For example, 1, 2, 3, and 4 are consecutive integers.

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How do you find the sum of consecutive integers?

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To find the sum of 'n' consecutive integers starting from 'a', use the formula: Sum = n/2 * (2a + (n-1)).

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What is the formula for the sum of 'n' consecutive even integers?

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The sum of 'n' consecutive even integers starting from '2a' is given by: Sum = n/2 * (2a + 2(n-1)).

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What is the formula for the sum of 'n' consecutive odd integers?

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The sum of 'n' consecutive odd integers starting from '2a + 1' is given by: Sum = n^2.

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If the sum of four consecutive integers is 180, how do you express the integers algebraically?

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Let the first integer be 'x'. The integers can be expressed as x, x+1, x+2, x+3. The equation is: x + (x+1) + (x+2) + (x+3) = 180.

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What is the relationship between the largest and smallest consecutive integers in a set of 'n' integers?

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In a set of 'n' consecutive integers, the largest integer is the smallest integer plus (n-1).

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How do you determine the middle number in a set of consecutive even integers?

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For 'n' consecutive even integers, the middle number can be found by taking the average of the first and last integers.

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What is the significance of the term 'consecutive' in mathematics?

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The term 'consecutive' indicates that numbers follow one after another in a specific order, which is crucial for solving problems involving sequences.

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How can you solve for an unknown integer in a sequence given the sum?

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Set up an equation based on the sum of the integers, then solve for the unknown variable.

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What is the sum of three consecutive integers if the sum is -30?

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Let the integers be x, x+1, x+2. The equation is: x + (x+1) + (x+2) = -30. Solve for x.