Arithmetic Sequence Calculator
An arithmetic sequence is a list of numbers where consecutive terms differ by a constant value called the common difference (d). Examples include: 2, 5, 8, 11... (d=3) or 10, 7, 4, 1... (d=−3).
- 1nth term: aₙ = a₁ + (n−1) × d
- 2Sum of n terms: Sₙ = n/2 × (2a₁ + (n−1)d) = n/2 × (first + last)
- 3If you know any two terms and their positions, you can find d
First term 3, difference 4, find 10th term=a₁₀ = 3 + 9×4 = 393, 7, 11, 15, 19, 23, 27, 31, 35, 39
Sum of first 100 natural numbers=5,050a₁=1, d=1, S₁₀₀ = 100/2 × (1+100) = 5,050
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Fun Fact
At age 10, Carl Friedrich Gauss instantly calculated the sum of 1 to 100 as 5,050 by pairing numbers (1+100, 2+99, ...) — this is exactly the arithmetic series formula.
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