a_n=a_1+(n-1)dVariables
- Define every symbol and unit before substitution.
- Check the domain, shape, and convention required by the formula.
How to use this formula
Computes the nth term of an arithmetic sequence.
Important notes
- Verify assumptions and units before applying the expression.
- Keep exact values until the final rounding step when possible.
Quick example
Use the arithmetic sequence term with a small known example, then verify the result independently.
Applicability, worked calculation, and verification
Domain and applicability
Apply Arithmetic Sequence Term only when the listed variables are defined, denominators are nonzero, and the problem satisfies the assumptions stated on this page.
Assumptions and domain checks
- For the Arithmetic Sequence Term, verify assumptions and units before applying the expression.
- For the Arithmetic Sequence Term, all variables must lie in the stated domain, and every denominator or inverse operation must be defined.
Boundary and special cases
- For Arithmetic Sequence Term, check zero, negative, and extreme input values before relying on the result.
- When using Arithmetic Sequence Term, confirm that denominators, radicals, logarithms, and domain restrictions remain valid for the chosen values.
Equivalent and alternative forms
- Keep the canonical LaTeX form a_n=a_1+(n-1)d for copying; rearrange only after preserving equivalence and domain restrictions.
Worked example
Worked setup for Arithmetic Sequence Term: Use the arithmetic sequence term with a small known example, then verify the result independently. The Arithmetic Sequence Term calculation should preserve its original grouping and record the final unit or interpretation.
- Identify every input required by Arithmetic Sequence Term and confirm that each value matches the variable definition and domain.
- Substitute the values into the complete expression a_n=a_1+(n-1)d without dropping parentheses, signs, powers, or branches.
- Evaluate Arithmetic Sequence Term in a stable order, preserve sufficient precision, and write the result together with its unit or mathematical interpretation.
- Verify the result independently by substitution, dimensional analysis, a limiting case, or an equivalent form appropriate to Algebra.
Independent verification
Check Arithmetic Sequence Term by substituting the result back into the defining relation when possible, confirming units or dimensions, and testing a simple limiting or known case.
Common mistakes
- Before substituting values into Arithmetic Sequence Term, map each variable to its definition and preserve every sign, exponent, subscript, and grouping mark.
- For the Arithmetic Sequence Term, check the final value in the original equation; algebraic rearrangement can introduce or lose solutions when domains are restricted.
Continue the workflow
Use Arithmetic Sequence Term in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
a_n=a_1+(n-1)d. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-26
Review method: Reviewed the notation, variable definitions, applicability conditions, worked workflow, and verification method for Arithmetic Sequence Term.
Verified against: OpenStax Algebra and Trigonometry
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Arithmetic Sequence Term used for?
Computes the nth term of an arithmetic sequence.
Can I copy this formula as LaTeX?
Yes. Copy a_n=a_1+(n-1)d or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.