Arithmetic & Geometric Sequence Calculator NZ

This calculator finds the nth term and the sum of both arithmetic and geometric sequences from the same inputs, so you can compare the two side by side. Sequences are ordered lists of numbers that follow a rule, and two types dominate school and university maths. An arithmetic sequence adds a fixed amount, the common difference, to get from one term to the next, like 2, 5, 8, 11. A geometric sequence multiplies by a fixed amount, the common ratio, each step, like 3, 6, 12, 24. They behave very differently: arithmetic sequences grow steadily in a straight line, while geometric sequences grow, or shrink, exponentially, which is why geometric series describe compound interest, population growth and radioactive decay. For each type there are two key questions: what is the nth term, and what is the sum of the first n terms. You enter the first term, the common difference for the arithmetic case, the common ratio for the geometric case, and the number of terms, and the calculator returns the arithmetic nth term and sum, and the geometric nth term and sum, all at once. Seeing both together makes the contrast clear and lets you use whichever you need. The results update as you type. Use it for homework, to check a series calculation, or to model steady versus compounding growth. The standard formulas are used: the arithmetic term and sum, and the geometric term and the geometric series sum, which is valid for any ratio other than one. The arithmetic is exact for your inputs, rounded for display where needed.

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Arithmetic adds the common difference; geometric multiplies by the common ratio. Both shown from the same inputs. Rounded for display.