What makes a sequence arithmetic

An arithmetic sequence changes by a constant difference dd from one term to the next.

That gives the nth-term rule an=a1+(n1)da_n = a_1 + (n-1)d and the sum rule S_n = rac{n}{2}(2a_1 + (n-1)d).

The preview cards make that repeated step visible instead of leaving the pattern hidden inside a formula.

Typical uses

  • Homework involving arithmetic progressions.
  • Checking repeated equal increments in savings, scoring, or staircase-style patterns.
  • Verifying partial sums before writing a closed-form solution.