Arithmetic sequence missing term calculator
In 4, 7, ?, 13, 16 every step is 3, so the missing third term is 10. Mark the gap with a question mark and get the missing value, its position, the step and the whole sequence filled in. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Sequence
- 4, 7, ?, 13, 16
- Missing term
- 10
- Missing index
- 3
- Common difference
- 3
- Completed sequence
- 4, 7, 10, 13, 16
An arithmetic sequence changes by the same amount at every step. This calculator fills one missing term marked with a question mark, x, or underscore, checks the surrounding values, and returns the completed pattern. Enter terms separated by commas or spaces. You may supply the common difference directly, or let the calculator infer it from the known positions. Increasing, decreasing, constant, negative, and decimal sequences are supported. The result identifies the missing term and its one-based position, reports the difference used, and includes the completed sequence for a quick visual check.
How a missing arithmetic term is determined
Every arithmetic sequence has a constant common difference, usually written as d. Moving one position to the right adds d, while moving one position to the left subtracts d. That makes a missing term recoverable from any known term when the distance between their positions is known.
For example, in 4, 7, ?, 13, 16, the difference is 3, so the third term must be 10. The calculator uses positions as well as values, which matters when the blank separates two known terms. If 5, ?, 13 is entered, the total change of 8 occurs across two steps, so each step is 4 and the blank is 9.
In ?, 6, 10, the difference is 4 and the first term is 2. This positional approach is more reliable than simply averaging neighbors because it also handles blanks at either end and validates every supplied value against one shared linear pattern.
Entering the sequence and common difference
Write at least three terms and use exactly one missing marker: ?, x, or _. Separate terms with commas, spaces, or semicolons. Numeric terms may be integers, negatives, decimals, or scientific notation, provided each value is finite.
A typical entry is 12, 9, x, 3, 0. If you omit it, the calculator infers d from the first two known positions and then verifies all remaining known terms. If you supply it, that value becomes the rule and every visible term must agree with it.
Inconsistent data is rejected instead of producing a plausible-looking answer. For example, 2, 5, ?, 12 cannot be arithmetic because the known positions do not share one constant step. Exactly one marker is required, and inputs with no blank, multiple blanks, fewer than three positions, nonnumeric visible terms, or more than one thousand positions return an invalid-input error.
Reading and checking the result
Check the output by subtracting each term from the next: every subtraction should equal the reported common difference. With decreasing sequences the difference is negative, as in 20, 15, ?, 5, where the answer is 10 and d is negative 5. With a constant sequence, d is zero and the missing value equals every other term.
Decimal calculations use finite JavaScript numbers and normalize routine floating-point noise, but the tool is not symbolic algebra and does not accept fractions written as 1/3.
What you can do with it
Check algebra homework
Confirm a missing value in an increasing, decreasing, constant, or decimal arithmetic progression and inspect the completed sequence.
Create answer keys
Generate deterministic answers for worksheets that hide one term while rejecting source questions whose visible values are inconsistent.
FAQ
Can the missing term be at the beginning or end?
Yes. The calculator extends the common difference backward for a missing first term or forward for a missing last term.
Do I have to enter the common difference?
No. It is inferred from known terms when omitted. Enter it when the difference is given explicitly or when you want the sequence checked against it.
Which symbols can mark the missing term?
Use exactly one question mark (?), x, or underscore (_). Uppercase X is also accepted.
Are negative and decimal values supported?
Yes. Terms and the common difference may be negative, zero, or decimal finite numbers. Fraction strings such as 1/3 are not supported.
What happens if the known terms do not fit one pattern?
The entry is refused rather than given a plausible-looking answer. In 2, 5, ?, 12, for example, the known positions cannot share one constant step, so there is no arithmetic answer.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/algebra/arithmetic-missing-term \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"sequence":"4, 7, ?, 13, 16"}'const res = await fetch("https://api.kit.forhosting.com/algebra/arithmetic-missing-term", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"sequence": "4, 7, ?, 13, 16"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/algebra/arithmetic-missing-term",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"sequence": "4, 7, ?, 13, 16"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/algebra/arithmetic-missing-term", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"sequence":"4, 7, ?, 13, 16"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"sequence":"4, 7, ?, 13, 16"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/algebra/arithmetic-missing-term", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"sequence": "4, 7, ?, 13, 16"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "algebra.arithmetic_missing_term",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How a missing arithmetic term is determined
A blank at an endpoint works by extending the same rule backward or forward.
Entering the sequence and common difference
The optional common_difference field is useful when a worksheet states d explicitly or when you want the result checked against a required step.
Reading and checking the result
The primary result is missing_term, the value that preserves the arithmetic pattern. missing_index uses ordinary one-based counting, so an index of 1 means the first displayed position rather than an internal zero-based array offset. common_difference shows the step that was supplied or inferred, and completed_sequence replaces the marker with the calculated value while retaining all known terms. The browser calculation is free and uses the same deterministic function as the API; successful API requests use the published base price of $0.002 per item.
Integration use cases
Validate stepped data
Recover one absent level in an evenly spaced schedule, measurement series, pricing ladder, or synthetic test fixture.
Technical questions
What happens if the known terms are inconsistent?
The request returns invalid_input because no single common difference can produce all of the visible terms at their stated positions.