How this calculator works
An arithmetic sequence changes by the same difference at each step. Two known terms determine that difference by dividing their value gap by their index gap. Once the first term is known, every indexed term follows directly. The table may skip indices using the increment; its sum includes only the rows displayed, not any skipped terms.
Formula
aₖ = a₁ + (k-1)d. From two terms: d = (aₙ-aₘ)/(n-m). For N consecutive terms, S = N(first + last)/2.
Worked example
Starting at 3 with difference 4 gives 3, 7, 11, 15, 19, whose sum is 55. If a₂ = 5 and a₅ = 14, the difference is 9/3 = 3 and the first term is 2.
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Frequently asked questions
Can the difference be negative or zero?
Yes. A negative difference gives a decreasing sequence; zero repeats the first term.
What if the final index is not reached by the increment?
The table stops at the largest selected index no greater than the final index.
Why must known indices differ?
A single index cannot determine a common difference from two values. Equal indices either repeat the same fact or contradict it.