Math Problem Statement

Find the next term in the sequence: -7, -5, 5, 2, 0, 0, -3, -1, 3, 0, ...

Solution

The sequence in the image provided is:

7,5,5,2,0,0,3,1,3,0,-7, -5, 5, 2, 0, 0, -3, -1, 3, 0, \dots

It appears that we are tasked with finding the next number in the pattern.

Step-by-step pattern analysis:

Let's break down the sequence into smaller steps:

  1. Difference between consecutive terms:
    • From 7-7 to 5-5 is an increase of +2+2.
    • From 5-5 to 55 is an increase of +10+10.
    • From 55 to 22 is a decrease of 3-3.
    • From 22 to 00 is a decrease of 2-2.
    • From 00 to 00 is a change of 00 (no change).
    • From 00 to 3-3 is a decrease of 3-3.
    • From 3-3 to 1-1 is an increase of +2+2.
    • From 1-1 to 33 is an increase of +4+4.
    • From 33 to 00 is a decrease of 3-3.

So, the differences form this pattern: +2,+10,3,2,0,3,+2,+4,3+2, +10, -3, -2, 0, -3, +2, +4, -3.

  1. Next step prediction:
    • The difference between 33 and 00 was 3-3.
    • The next step should follow a similar repeating pattern. If we continue from the observed differences, the next difference should be an increase of +2+2 (following the earlier increase pattern).

Thus, the next term after 00 should be 0+2=20 + 2 = 2.

Conclusion:

The next number in the sequence is 22.

The correct answer is B. 2.

Would you like more details or have any questions? Here are five related questions to consider:

  1. How can you identify the general form of a sequence?
  2. What are the common types of sequences found in mathematics?
  3. Can this sequence be expressed as a combination of arithmetic and geometric progressions?
  4. How does pattern recognition help in solving real-world problems?
  5. What other methods can be used to predict unknown terms in a sequence?

Tip: Always look for repeating patterns in differences between consecutive terms when working with non-standard sequences.

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Math Problem Analysis

Mathematical Concepts

Sequence
Pattern Recognition
Arithmetic Sequence

Formulas

Difference between consecutive terms

Theorems

Pattern Recognition Theorem

Suitable Grade Level

Grades 8-10