Arithmetic and geometric progressions

The two most important families of sequences in elementary arithmetic: the arithmetic progression, in which at each step a fixed common difference $d$ is added, and the geometric progression, in which one multiplies by a fixed common ratio $q$. For both, the closed form of the $n$-th term and the formula for the sum of the first $n$ terms are derived, illustrated by the anecdote of Gauss and the legend of the chessboard, and linked to the comparison between simple interest and compound interest.

• Arithmetic progression
• Sum of the first n terms of an AP
• The anecdote of the young Gauss
• Geometric progression
• Sum of the first n terms of a GP
• The legend of the chessboard
• AP and GP compared
• GP and geometric series