MATHEMATICS · FREE TOOL

Arithmetic Sequence Calculator

Enter the first term, the common difference, and n — get the nth term, the sum, the full sequence, and the step-by-step working behind every number. Free, instant, and entirely in your browser.

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Four modes, live results — everything computes on this page as you type. Switch modes below; shared values carry over.

Where the sequence starts — decimals and negatives welcome.

The fixed step between terms — negative or zero is fine.

Whole number from 1 to 999,999,999.

STEPS
RESULTS — SEQUENCE & SUM

Sequence

Number line

Formula

Step by step

    QUICK REFERENCE

    The three formulas doing the work

    Every mode of the calculator above reduces to one of these. Memorise the first two and you can rebuild the rest on a napkin.

    Any term

    an = a1 + (n − 1)·d

    Jump straight to any position. With a1 = 3 and d = 4, the 20th term is 3 + 19·4 = 79.

    Sum of n terms

    Sn = n/2 · (a1 + an)

    n times the average of the first and last term — the shortcut Gauss used to total 1 … 100 in one line: 50 · 101 = 5050.

    Common difference

    d = (aj − ai) / (j − i)

    Pick any two terms, subtract, divide by the gap in positions. For consecutive terms, just subtract.

    HOW TO USE

    Four steps, about ten seconds

    Everything updates live as you type — no Calculate-then-wait round trips.

    STEP 01

    Pick a mode

    Sequence & Sum is the default. Which Term? locates a value inside a sequence, Partial Sum totals a stretch between two positions, and Difference recovers d from two known terms.

    STEP 02

    Enter your numbers

    First term a1, common difference d, and n — or that mode's inputs. Decimals and negatives are welcome; d = 0 gives a constant sequence, a negative d a decreasing one.

    STEP 03

    Read the results

    Key answers up top, the full sequence as chips, a number-line plot, the formula with your numbers substituted in, and step-by-step working ready to lift into homework.

    STEP 04

    Tune and export

    Choose decimal precision, switch the steps off for a cleaner panel, and hit the copy button for a plain-text summary of the whole calculation.

    Inputs are validated as you type — if n isn't a whole number or p outruns q, the calculator says exactly what to fix instead of guessing.

    FAQ

    Arithmetic sequence questions, answered

    The eight questions that show up most in homework, exams, and our inbox.

    What is an arithmetic sequence?+
    An arithmetic sequence (or arithmetic progression) is a list of numbers in which each term after the first is made by adding the same fixed number — the common difference d — to the term before it. For example, 3, 7, 11, 15, 19, … is arithmetic with a1 = 3 and d = 4, because every gap between terms is exactly 4.
    How do I find the nth term of an arithmetic sequence?+
    Use an = a1 + (n − 1)·d. With a1 = 3 and d = 4, the 20th term is a20 = 3 + 19·4 = 79. The calculator's default mode substitutes your numbers automatically and shows the working line by line.
    What is the formula for the sum of the first n terms?+
    Sn = n/2 · (2a1 + (n − 1)·d), or the friendlier Sn = n/2 · (a1 + an) once you know the last term — n times the average of the first and last terms. That's the shortcut Gauss used to total 1 through 100 in one line: 100/2 · (1 + 100) = 5050.
    How do I find the common difference?+
    Subtract any two terms and divide by the distance between their positions: d = (aj − ai)/(j − i). If the 1st term is 5 and the 10th is 41, then d = (41 − 5)/(10 − 1) = 4. For consecutive terms it's just subtraction: d = an − an−1.
    Can the common difference be negative or zero?+
    Yes. A negative d produces a decreasing sequence (100, 93, 86, …), and d = 0 produces a constant one (4, 4, 4, …) — both count as arithmetic. The difference can also be a decimal or fraction, like 0.25; the calculator handles all of these.
    How can I check whether a number belongs to a sequence?+
    Solve n = (x − a1)/d + 1. If n comes out as a positive whole number, x is the nth term; if not, it never appears. The Which Term? mode does this for you and, when the answer is no, shows the two nearest terms on either side.
    What's the difference between an arithmetic and a geometric sequence?+
    Arithmetic sequences add a fixed number each step — a constant difference. Geometric sequences multiply by a fixed number — a constant ratio. So 2, 5, 8, 11 is arithmetic with d = 3, while 2, 6, 18, 54 is geometric with ratio 3.
    Does this calculator store or upload my inputs?+
    No. Every calculation runs locally in your browser — nothing you type is uploaded, logged, or saved anywhere. Once the page has loaded, the calculator even works with your internet connection off.