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Practice Solving Consecutive Integer Problems

Site: Saylor University
Course: [CB DRAFT] MA007: Real World Math: Algebra
Book: Practice Solving Consecutive Integer Problems
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Date: Tuesday, 27 October 2026, 3:27 PM

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Table of contents

Practice Problems

  1. The sum of ‍5 consecutive odd numbers is ‍135.

    What is the second number in this sequence?

  2. The sum of ‍6 consecutive integers is 393.

    What is the second number in this sequence?

  3. The sum of ‍3 consecutive even numbers is 270.

    What is the second number in this sequence?

  4. The sum of ‍4 consecutive integers is 326
    What is the second number in this sequence?

Source: Khan Academy, https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations/linear-equations-word-problems/e/integer_sums
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Answers

  1. Call the first number in the sequence $$x$$.

    The next odd number in the sequence is $$x+2$$.

    The sum of the 5 consecutive odd numbers is:

    $$x+ (x + 2)+ (x + 4)+ (x + 6)+ (x + 8) = 135$$

    $$5x + 20= 135$$

    $$5x = 115$$

    $$x = 23$$

    Since $$x$$ is the first number, $$x+2$$ is the second odd number.

    Thus, the second number in the sequence is 25.

  2. Call the first number in the sequence $$x$$.

    The next integer in the sequence is $$x+1$$

    The sum of the 6 consecutive integers is:

    $$x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 393$$

    $$6x + 15= 393$$

    $$6x = 378$$

    $$x = 63$$

    Since $$x$$ is the first number, $$x+2$$ is the third integer.

    Thus, the third number in the sequence is 65.

  3. Call the first number in the sequence $$x$$.

    The next integer in the sequence is $$x+2$$

    The sum of the 3 consecutive even numbers is:

    $$x+ (x + 2)+ (x + 4) = 270$$

    $$3x + 6= 270$$

    $$3x = 264$$

    $$x = 88$$

    Thus, the first number is 88.

  4. Call the first number in the sequence $$x$$.

    The next integer in the sequence is $$x+1$$

    The sum of the 4 consecutive integers is:

    $$x+ (x + 1)+ (x + 2)+ (x + 3) = 326$$

    $$4x + 6= 326$$

    $$4x = 320$$

    $$x = 80$$

    Since $$x$$ is the first number, $$x+1$$ is the third integer.

    Thus, the third number in the sequence is 81.