Arithmetic Sequence Calculator
Find the nth term, common-difference pattern, and partial sum of an arithmetic sequence with full step-by-step explanation.
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What this calculator teaches
An arithmetic sequence changes by adding the same number each time. That repeated addition creates a linear pattern.
Students use arithmetic sequences for pattern problems, seating rows, savings plans, and any situation with equal increases or decreases.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| nth term | a_n = a_1 + (n - 1)d | Finds the term in position n. |
| partial sum | S_n = n(a_1 + a_n)/2 | Adds the first n terms. |
Step-by-Step Examples
- Let a₁ = 5 and d = 3.
- For n = 10, a₁₀ = 5 + (10 - 1)3.
- a₁₀ = 5 + 27 = 32.
- Use Sₙ = n(a₁ + aₙ)/2.
- S₁₀ = 10(5 + 32)/2.
- S₁₀ = 185.
Where students use this
Common Mistakes to Avoid
The first term already exists, so you add the difference only n − 1 times.
A sequence is the list of terms. A series is the sum of terms.
Only use arithmetic formulas when the same number is added each time.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.