Arithmetic Sequence Calculator

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Use this free Arithmetic Sequence Calculator to solve common sequence problems in seconds: compute the n-th term (also written as a_n), the sum of the first n terms (often written as S_n), the common difference (d), or even the first term (a₁) when other pieces are known. Everything runs in your browser—no login, no signup.

🧮Find a_n, S_n, d, or a₁

⚡Instant results + step-by-step explanation

📚Great for homework, exams & quick checks

📱Clean layout for screenshots & sharing

Enter your arithmetic sequence values

Choose what you want to solve, then enter the values you already know. Leave unknown fields blank if the mode doesn’t require them.

Solve for *

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First term (a₁)

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Common difference (d)

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Number of terms (n)

n-th term (aₙ)

Show first k terms (optional)

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Your result will appear here

Enter both names and tap “Calculate” to see your score.

Tip: Try a negative difference (like 10, 7, 4, 1, …) or a decimal difference (like 1.5, 2.0, 2.5, …).

Visual meter: not a score—just a quick sense of how large the computed value is.

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This calculator is for educational use. Double-check your course’s notation and rounding rules and should not be used for serious decisions about love, dating or marriage.

🧠Arithmetic sequence basics

What this calculator can solve

An arithmetic sequence increases (or decreases) by the same amount each step. This tool solves the most common “find the missing piece” problems instantly.

Find a_n using a_n = a₁ + (n−1)d.
Find S_n using S_n = n/2 · (2a₁ + (n−1)d).
Solve for d, a₁, or n when other values are known.

Pro tip: If your terms go 12, 9, 6, 3… your difference is d = −3. Negative d is still a perfectly valid arithmetic sequence.

✅Common pitfalls

Avoid these mistakes

Most arithmetic-sequence errors come from mixing up indices or using the wrong “sum” formula. Here’s a quick checklist before you submit homework or an exam answer.

(n − 1) counts “steps” from the first term to the n-th term.
If you know a₁ and a_n, the average term is (a₁ + a_n)/2.
For sums, don’t forget the n/2 factor.
Units matter: “$ per month” and “miles per day” should carry through.

❓ FAQ + examples

Examples, edge cases, and common questions

What is an arithmetic sequence in one sentence?
It’s a sequence where you add the same number (d) every time you move to the next term. If you keep subtracting the same number, that’s also arithmetic—just with a negative d.
How do I find the common difference?
Subtract consecutive terms: d = a₂ − a₁. If you don’t have consecutive terms but you do have a₁, a_n, and n, use d = (a_n − a₁)/(n − 1).
Worked example: Find the 25th term.
Sequence: 8, 13, 18, 23, … Here a₁ = 8 and d = 5. Then a₂₅ = 8 + (25 − 1)·5 = 128.
Worked example: Sum of the first 50 terms.
Using the sequence above, first compute a₅₀ = 8 + 49·5 = 253. Then S₅₀ = 50/2 · (8 + 253) = 25 · 261 = 6525.
What if d = 0?
Then every term is the same number (constant sequence). The n-th term is always a₁, and the sum is S_n = n·a₁. If you try to solve for n using n = 1 + (a_n − a₁)/d, it fails because dividing by 0 is undefined.
Can n be a non-integer?
In standard sequences, n is a positive integer because it counts terms. If your algebra produces a non-integer, the inputs may not describe a real arithmetic sequence, or the problem might include rounding/measurement tolerance.
How is an arithmetic sequence related to a linear function?
The n-th term formula is linear in n. If you graph (n, aₙ), you get a straight line with slope d. That’s why arithmetic sequences show up in slope and line-equation problems.
Why does the sum formula use n/2?
Pair first and last terms: each pair sums to a₁ + aₙ, and there are n pairs when you double the list. That creates 2Sₙ, so dividing by 2 gives the final sum.
Is this calculator okay for exam practice?
Yes—use it to verify your manual work. Best loop: solve by hand → verify here → write the steps cleanly in your notes.

Educational note: Some textbooks use t_n instead of a_n. The formulas are identical.

❓ FAQ

Frequently Asked Questions

How does the Soulmate Finder work?
The calculator turns the letters in both names into numbers, mixes them with a hidden “vibe” formula, and converts that into a 0–100 soulmate match score plus a short explanation.
Is this scientifically accurate?
No. This is a fun, non-scientific tool inspired by name numerology and playful compatibility quizzes. It’s made for entertainment only.
Will using nicknames change the result?
Yes. Different letters = different numbers = different soulmate score. That’s part of the fun – test full names, nicknames and “inside joke” names.
Does a low score mean we should break up?
Absolutely not. Real love is built on communication, trust and shared values. This calculator is just a fun ice-breaker, not relationship advice.

🚀 Viral study tip

Make this “shareable” in 10 seconds

For Shorts/Reels: show the sequence → tap Calculate → screenshot the steps. People share tools that instantly confirm homework answers (and look clean on mobile).

Good viral prompts

“If the first term is 7 and you add 4 each time… what’s the 50th term?”
“How much total after 30 days if you add $5 more each day?”
“This one formula saves you 5 minutes on every homework problem.”

MaximCalculator provides simple, user-friendly tools. Always treat results as entertainment and double-check any important numbers elsewhere.