An arithmetic series adds terms with a constant difference d.
Try this
5
Sₙ = 3 + 5 + 7 + 9 + … (a = 3, d = 2) = 35
Two ways to write the sum
a = first term, d = common difference. Pair the first and last terms — every pair sums to (first + last).
Your turn
Find 2 + 5 + 8 + … + 29.
Recap
- A series adds the terms of an arithmetic sequence.
- Sₙ = n/2 · (2a + (n−1)d), or just n/2 · (first + last).
- Gauss's trick: 1 + 2 + … + 100 = 50 · 101 = 5050.
Sum of first n terms
Try it
Sum 1 + 2 + 3 + ... + 100
n=100, a=1, d=1. S = 100/2 · (2 + 99) = 50 · 101 = 5050.