如何计算Sequences Series

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A sequences and series calculator finds nth terms and partial sums of arithmetic and geometric sequences — fundamental patterns in mathematics, finance, and science.

公式

Arithmetic sum: Sₙ = n/2 × (2a₁ + (n−1)d)

分步指南

1Arithmetic nth term: aₙ = a₁ + (n−1)d
2Arithmetic sum: Sₙ = n/2 × (2a₁ + (n−1)d)
3Geometric nth term: aₙ = a₁ × rⁿ⁻¹
4Geometric sum: Sₙ = a₁ × (1−rⁿ)/(1−r) (for r≠1)

例题解析

输入

Arithmetic: first term 3, difference 4, find 10th term and sum

结果

a₁₀ = 3 + 9×4 = 39; S₁₀ = 10/2 × (6+36) = 210

常见问题

What is Sequences And Series?

A sequences and series calculator finds nth terms and partial sums of arithmetic and geometric sequences — fundamental patterns in mathematics, finance, and science. Use this calculator for accurate, instant results.

How accurate is the Sequences And Series calculator?

The calculator uses the standard published formula for sequences and series. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Sequences And Series calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Sequences And Series calculator use?

The core formula is: Arithmetic nth term: aₙ = a₁ + (n−1)d. Each step in the calculation is shown so you can verify the result manually.