Arithmetic series sum

Find the sum of an arithmetic sequence: Sₙ = n/2 × (2a + (n−1)d) or Sₙ = n/2 × (first + last).

n (terms)

First term (a)Common diff (d)

Sₙ = n/2 × (2a + (n−1)d) or equivalently Sₙ = n/2 × (first + last).

Sum of first 10 terms, a=2, d=3: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29. S₁₀ = 10/2 × (2+29) = 5 × 31 = 155.

Sum of 1+2+3+...+n = n(n+1)/2. This is an arithmetic series with a=1, d=1.