Arithmetic sequences are fundamental in mathematics and appear in everyday problem‑solving. An arithmetic sequence is a list of numbers in which the difference between consecutive terms is constant. Knowing how to generate the first few terms is essential for tests, coding challenges, and real‑world data analysis.

Using a Known First Term and Common Difference

If the first term (a₁) and the common difference (d) are given, you can construct the sequence by repeatedly adding d. For example, with a₁ = 10 and d = 3:

• a₁ = 10
• a₂ = 10 + 3 = 13
• a₃ = 13 + 3 = 16
• a₄ = 16 + 3 = 19
• a₅ = 19 + 3 = 22
• a₆ = 22 + 3 = 25

Solving When the Formula Is Provided

Sometimes the sequence is defined by a general formula, such as:

a_n = 10 + (n-1) × 1.75

Here a_n represents the nth term. Substitute n = 2 through 6 to find each term:

1. n = 2: 10 + (2-1) × 1.75 = 11.75
2. n = 3: 10 + (3-1) × 1.75 = 13.50
3. n = 4: 10 + (4-1) × 1.75 = 15.25
4. n = 5: 10 + (5-1) × 1.75 = 17.00
5. n = 6: 10 + (6-1) × 1.75 = 18.75

These methods give you the first six terms quickly and reliably.

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