Arithmetic Series Sum
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The sum of an arithmetic series is the average of the first and last terms times the number of terms — the trick young Gauss reportedly used to add 1 through 100 in seconds: S = (100/2)(1 + 100) = 5050. In the general form, the last term is unpacked as a₁ + (n − 1)d.
It answers stacking questions directly: a log pile with 15 logs on the bottom row and one fewer per row for 10 rows holds S = (10/2)(2 × 15 + 9 × (−1)) = 105 logs.
Arithmetic Series Sum
Where
- = Sum of the first n terms
- = Number of terms
- = First term
- = Common difference
Missing one of these? Work it out first, then come back
- Sum of the first n terms — Geometric Series Sum, Arithmetic Mean of Two Numbers
- Number of terms — Geometric Series Sum, Slope Between Two Points
- First term — Arithmetic Sequence nth Term, Geometric Sequence nth Term
- Common difference — Arithmetic Sequence nth Term, Geometric Sequence nth Term