Mathematics · Precalculus
Arithmetic Sequence Calculator
Find the nth term of a sequence with a constant difference.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- From term 1 to term 10 there are 9 jumps.
- Change = 9 × 3 = 27.
- a_10 = 5 + 27 = 32.
Understand Arithmetic sequence
One idea, three depths
Choose how deeply to explain Arithmetic sequence
Arithmetic sequence: Find the nth term of a sequence with a constant difference.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Arithmetic sequence to answer this question: find the nth term of a sequence with a constant difference? Enter First term, Common difference, Term number n; the calculator shows nth term. For example: With first term 5 and difference 3, term 10 is 5+9×3=32. The answer tells you nth term.
Age 15Explain it to a 15-year-oldConnect it to the formula
There are n−1 equal jumps from the first term to the nth term, each adding the common difference d. The rule is aₙ = a₁ + (n−1)d. Its input values are First term, Common difference, Term number n, and the main result is nth term. For example: With first term 5 and difference 3, term 10 is 5+9×3=32.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated arithmetic sequence relation over the valid mixed integer and real-number domain stated below. The implemented relation is aₙ = a₁ + (n−1)d, evaluated from First term, Common difference, Term number n to produce nth term. There are n−1 equal jumps from the first term to the nth term, each adding the common difference d. Use n−1 differences because the first term occurs before any jump.
Inputs and valid domain
- First term must be a finite real number.
- Common difference must be a finite real number.
- Term number n must be an integer, at least 1.
Important boundary: Use n−1 differences because the first term occurs before any jump.
The formula
aₙ = a₁ + (n−1)d
How the calculator works through it
It substitutes First term, Common difference, Term number n into the formula and exposes every numerical step above. The main output is nth term, accompanied by Number of jumps.
Read the result correctly
The nth term is the direct answer to “find the nth term of a sequence with a constant difference.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
With first term 5 and difference 3, term 10 is 5+9×3=32.
Where this model stops being reliable
Use n−1 differences because the first term occurs before any jump.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Arithmetic sequence works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Arithmetic sequence uses aₙ = a₁ + (n−1)d. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Functions, domains and ranges
Domain and range language helps you identify which Arithmetic sequence inputs are valid and how the output behaves.
Review this foundation about 6 min
Optional enrichment
- Exponential growth and decay
Exponential models provide a useful extension when Arithmetic sequence is applied to multiplicative change.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read First term, Common difference, Term number n.
- Evaluate the principal relationship: aₙ = a₁ + (n−1)d.
- Return nth term and check the domain conditions described above.
Python
from math import *
def arithmetic_sequence(a, b, n) -> float:
return (a + ((n - 1.0) * b))
assert abs(arithmetic_sequence(5, 3, 10) - 32) < 1e-6 * max(1.0, abs(32))
C
#include <assert.h>
#include <math.h>
double arithmetic_sequence(double a, double b, double n) {
return (a + ((n - 1.0) * b));
}
int main(void) {
const double expected = 32;
const double actual = arithmetic_sequence(5, 3, 10);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double arithmetic_sequence(double a, double b, double n) {
return (a + ((n - 1.0) * b));
}
int main() {
constexpr double expected = 32;
const double actual = arithmetic_sequence(5, 3, 10);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double arithmetic_sequence(double a, double b, double n)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global arithmetic_sequence
section .text
arithmetic_sequence:
push rbp
mov rbp, rsp
sub rsp, 64
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd [rbp-24], xmm2
mov rax, 0x3ff0000000000000
movq xmm0, rax
movsd [rbp-56], xmm0
movsd xmm0, [rbp-24]
subsd xmm0, [rbp-56]
movsd [rbp-48], xmm0
movsd xmm0, [rbp-48]
mulsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-8]
addsd xmm0, [rbp-40]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
leave
ret
MATLAB
function result = arithmetic_sequence(a, b, n)
result = (a + ((n - 1.0) * b));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_, n_] := (a + ((n - 1.0) * b));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Arithmetic Sequence Calculator. MW SysArc Tools. https://math.mwsysarc.com/precalculus/arithmetic-sequence-calculator
MLA 9
MW SysArc. “Arithmetic Sequence Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/precalculus/arithmetic-sequence-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Arithmetic Sequence Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/precalculus/arithmetic-sequence-calculator.
Harvard
MW SysArc (2026) ‘Arithmetic Sequence Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/precalculus/arithmetic-sequence-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_arithmetic_sequence_2026,
author = {{MW SysArc}},
title = {Arithmetic Sequence Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/precalculus/arithmetic-sequence-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Arithmetic Sequence Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/precalculus/arithmetic-sequence-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Arithmetic sequence do?
Find the nth term of a sequence with a constant difference.
How does the Arithmetic sequence work?
The calculator applies aₙ = a₁ + (n−1)d. There are n−1 equal jumps from the first term to the nth term, each adding the common difference d.
What can I learn from the Arithmetic sequence?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .