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Consecutive Integers Consecutive Integers are integers that follow one after another. Example 1: are consecutive integers.

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In Algebra we sometimes are presented with a problem that requires a pattern of consecutive integers. The patterns are usually one of three types: 1) Consecutive Integers 2) Consecutive Even Integers 3) Consecutive Odd Integers

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Consecutive Integers Consider the example given earlier: Given the first integer 8, what would be necessary to determine the next integer of 9? Simply add 1 to the 8 to give: Add 2 to the 8 to get the next integer 10:

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Consecutive Integers What if the first integer is unknown? Let x represent the first integer. Simply add 1 to get the second integer. Add 2 to get the third integer.

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Consecutive Integers Assume that we are considering three consecutive integers, and do not know the first integer. The pattern is given by: Example 2: Now assume that we know the first integer is 17. The integers are …

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**Consecutive Even Integers Consecutive Odd Integers**

Consecutive even integers and consecutive odd integers will be considered together since they are related. Consecutive Even Integers: Consecutive Odd Integers:

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**Consecutive Even Integers Consecutive Odd Integers**

Notice the common pattern for the second integer: Increase by 2 Increase by 2

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**Consecutive Even Integers Consecutive Odd Integers**

Notice the common pattern for the third integer: Increase by 4 Increase by 4 Note that it is the first integer that determines the pattern of even or odd.

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**Consecutive Even Integers Consecutive Odd Integers**

Assume that we are considering three consecutive even integers, or three consecutive odd integers, and do not know the first integer. Both patterns are given by:

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Example 3: Write the pattern for three consecutive odd integers: Determine the integers if the first integer is -7:

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Do-Now 1)3x 2 – 20x – 7 = 0 2)x 2 + 2x + 1 = 0 3)x 2 – 100x – 204 = 0 4)2x 2 + 9x + 9 = 0 Factor each of the following.Now solve each of them. (3x + 1)(x.

Do-Now 1)3x 2 – 20x – 7 = 0 2)x 2 + 2x + 1 = 0 3)x 2 – 100x – 204 = 0 4)2x 2 + 9x + 9 = 0 Factor each of the following.Now solve each of them. (3x + 1)(x.

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