Math Problem Statement
50, 25, 0, -25, -50
Solution
The sequence provided: 50, 25, 0, -25, -50 appears to be an arithmetic sequence. Let's break it down:
- The first term (a₁) is 50.
- The second term (a₂) is 25.
- The third term (a₃) is 0.
- The fourth term (a₄) is -25.
- The fifth term (a₅) is -50.
To confirm it's an arithmetic sequence, we check if the difference between consecutive terms is constant.
Since the common difference (d) is -25, this is indeed an arithmetic sequence with a common difference of -25.
The general formula for the -th term of an arithmetic sequence is:
Here:
Thus, the general term for the sequence is:
Would you like to explore any specific details about this sequence?
Here are some related questions to consider:
- What would be the 10th term in this arithmetic sequence?
- How can you find the sum of the first 20 terms of the sequence?
- Can you find the formula for the sum of this arithmetic sequence?
- What are some real-world examples of arithmetic sequences like this one?
- How does this sequence compare to a geometric sequence?
Tip: The common difference in arithmetic sequences can also help you easily find any term, without listing all the preceding ones!
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Algebra
Formulas
General formula for an arithmetic sequence: a_n = a_1 + (n-1) * d
Theorems
Arithmetic Sequence Common Difference Theorem
Suitable Grade Level
Grades 7-9