Your Sequence Toolkit

A constant step is a surprisingly powerful thing. Here is everything an arithmetic sequence hands you:

• The common difference d is the fixed gap between terms
• The nth-term formula, aₙ = a₁ + (n − 1)d, jumps to any position at once
• Plotted, the terms always fall on a straight line
• The series formula, n/2 × (first + last), totals them in one step

Spot the steady gap, and a long list of numbers stops being a chore and starts being predictable.