Math Problem Statement
Find x so that x+1, x-1, and 2x are terms of an arithmetic sequence. Write out the terms
Solution
For , , and to be terms of an arithmetic sequence, the difference between consecutive terms must be the same. This gives us the condition:
Step 1: Simplify the equation
The first term on the left side simplifies as:
The right side simplifies as:
Step 2: Set up the equation
Now we equate the two expressions:
Step 3: Solve for
Subtract 1 from both sides:
Step 4: Verify the terms
Substitute into the terms:
The terms are , , and . The common difference is , confirming that the terms form an arithmetic sequence.
Thus, , and the terms are , , and .
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Related Questions:
- What are the general conditions for numbers to form an arithmetic sequence?
- How would the problem change if the sequence was geometric?
- How do you find the sum of an arithmetic sequence?
- Can an arithmetic sequence have increasing terms if one term is negative?
- How does solving for terms in an arithmetic sequence apply to real-world scenarios?
Tip:
When working with sequences, always check for the common difference (arithmetic) or ratio (geometric) to confirm the type of sequence.
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Math Problem Analysis
Mathematical Concepts
Algebra
Arithmetic Sequences
Formulas
Arithmetic sequence difference: d = a(n+1) - a(n)
Theorems
Properties of Arithmetic Sequences
Suitable Grade Level
Grades 8-10
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