which of the following is an arithmetic sequence

Guri Bee

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18-10-2024

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Unraveling the Mystery: Identifying Arithmetic Sequences

In the world of mathematics, sequences are ordered lists of numbers that follow specific rules. One such sequence is the arithmetic sequence, where each term is found by adding a constant value (known as the common difference) to the previous term.

But how do we identify an arithmetic sequence? Let's dive into the details using examples from GitHub discussions:

Question: "Which of the following is an arithmetic sequence?

1. 2, 4, 6, 8, 10
2. 1, 3, 5, 7, 9
3. 1, 2, 4, 8, 16
4. 2, 4, 8, 16, 32"

Answer: (From a GitHub discussion by user "MathLover123"): "The correct answer is both options 1 and 2. In option 1, the common difference is 2 (4-2 = 2, 6-4 = 2, and so on). In option 2, the common difference is also 2 (3-1 = 2, 5-3 = 2, and so on)."

Analysis: Both sequences 1 and 2 have a constant difference between terms, confirming them as arithmetic sequences.

Why are options 3 and 4 not arithmetic sequences?

Option 3: The difference between terms is not constant (2-1 = 1, 4-2 = 2, 8-4 = 4), thus it is not an arithmetic sequence.

Option 4: Similar to option 3, the difference between terms is not constant (4-2 = 2, 8-4 = 4, 16-8 = 8).

A Real-World Analogy:

Imagine you're saving money. You decide to deposit $5 every week. This scenario forms an arithmetic sequence. Your savings after each week would be:

• Week 1: $5
• Week 2: $10 (5 + 5)
• Week 3: $15 (10 + 5)
• Week 4: $20 (15 + 5)

Key Takeaway:

To identify an arithmetic sequence, look for a constant difference between consecutive terms. This consistent pattern is what defines an arithmetic sequence. Remember, a sequence can only be considered arithmetic if this constant difference is present throughout the entire sequence.