Quick answer

Enter a₁, d, and n to list labeled terms with a step-by-step solution panel. All processing stays in your browser.

Formula

  • aₖ = a₁ + (k - 1)d
  • Up to n = 50 whole-number terms

Introduction

The calculator lives at the top of the home page so you can compute before reading longer explanations. That placement matches how most students work: try numbers first, then read why the list behaves.

If you want the manual method first, read how to find arithmetic sequence terms and use this guide as a checker.

Example sets with different signs of d appear in arithmetic sequence examples so you can compare paper work with on-screen output.

Inputs explained

First term a₁ sets the starting value. Enter decimals when the problem uses fractional starts.

Common difference d sets the step. Negative values create decreasing lists without changing the interface.

Number of terms n sets how many labeled rows appear. n must be a whole number from 1 to 50 for this tool.

The result panel shows a₁ through aₙ with subscripts. The solution panel narrates the same logic you would write in class.

What the tool computes

  • Each row: aₖ = a₁ + (k - 1)d
  • Solution steps mirror substitution and verification

The list updates as you type. There is no submit button and no server round trip, which keeps the tool usable on slow connections.

Use the solution block to study order of operations: identify a₁, state d, apply the index form, then sanity-check the last term.

When a problem also asks for a sum, list terms here first, then apply the series formula from the sum article in this blog.

Step-by-step guide

  1. Open the home page. Scroll to the calculator block with id calculator if you landed elsewhere.
  2. Enter a₁, d, and n. Use the same units the problem uses; keep signs with negative d.
  3. Read labeled results. Copy subscript labels directly into homework or a spreadsheet column.
  4. Study the solution panel. Compare each sentence with your handwritten steps.
  5. Adjust and recheck. Change one input at a time to see how the list shifts.

Sample calculation

Try a₁ = 1, d = 3, n = 4. You should see 1, 4, 7, 10 with matching subscripts.

Change d to -3 while keeping a₁ = 1 and n = 4 to watch the list decrease: 1, -2, -5, -8.

Those two quick trials reinforce how sign controls direction without changing the formula structure.