Math Problem Statement

Enter the next two terms of the sequence: 34, 30, 28, 26, 30, ?, ?

Solution

The given sequence in the image is:

34,30,28,26,30,?,?34, 30, 28, 26, 30, \, ? , \, ?

Let's analyze the pattern:

  • From 34 to 30: Subtract 4
  • From 30 to 28: Subtract 2
  • From 28 to 26: Subtract 2
  • From 26 to 30: Add 4

So, it seems the pattern alternates between subtracting 4, subtracting 2, subtracting 2, and then adding 4. Following this pattern:

  • From 30: The next step would be subtracting 4, so the next term is 304=2630 - 4 = 26.
  • From 26: The next step would be subtracting 2, so the next term is 262=2426 - 2 = 24.

Thus, the next two terms in the sequence are 26 and 24.

Would you like more details or have any other questions?

Here are some related questions to explore further:

  1. What is a common method to identify patterns in arithmetic sequences?
  2. How can alternating operations (addition/subtraction) be used in number sequences?
  3. What is the difference between arithmetic and geometric sequences?
  4. How can you determine whether a sequence will continue indefinitely with a predictable pattern?
  5. Can we create a formula for this sequence to predict any term?

Tip: Always check for repeating patterns, such as alternating operations or consistent steps, when identifying sequences.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Pattern Recognition

Formulas

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Theorems

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Suitable Grade Level

Grades 5-7