Sequence Calculator

Spotting the Rule Behind a Sequence

Every number pattern follows a rule, and this calculator applies it, whether terms add, multiply, or borrow from neighbors. Exam candidates, programmers testing loop outputs, and puzzle fans predicting the next value all lean on it.

Terms and Totals Across Pattern Types

Geometric lists multiply by a fixed ratio instead of adding. The run 3, 6, 12, 24 doubles each step, so the fifth term is 3 x 2 x 2 x 2 x 2 = 48.

Summing works once the rule is known. Adding 3 + 6 + 12 + 24 + 48 gives 93, and the calculator reproduces that total for any doubling run.

Arithmetic runs reward the same treatment. With a Starting number of 5 and a Common difference of 4, the terms read 5, 9, 13, 17, 21, and setting n-th term to obtain to 10 returns 41, since 5 + 9 x 4 makes 41. Tallying the run uses the pair shortcut: half the term count times the first and last terms added, so 10 / 2 x 46 gives 230. The direction switch matters too, because entering 5 with Decreasing and the same difference walks the run backward to 5, 1, -3, and the tool tracks every negative step.

Steps for Generating Your Sequence

Under Sequence type pick Arithmetic, Geometric, or Fibonacci, and set Sequence direction to Increasing or Decreasing. Enter a Starting number, the Common difference for arithmetic runs, and the n-th term to obtain. Press Calculate and every term up to your target appears.

Tips: geometric growth outruns expectations quickly. Doubling a start of 3 five times reaches 96, so even a modest ratio explodes over long runs.