Geometric Progression

A sequence where the ratio

A sequence where the ratio of any term to its preceding term is constant (non-zero). This constant ratio is called the common ratio 'r'. For example:

The constant value by which each

The constant value by which each term is multiplied to get the next term. r = T(n+1)/Tn. It can be positive, negative, or fractional (but never zero).

Tn = ar^(n

Tn = ar^(n-1), where 'a' is the first term, 'r' is the common ratio, and 'n' is the position of the term. This helps find any term without calculating

When r = 1

When r = 1: Sn = na. When r ≠ 1: Sn = a(r^n - 1)/(r - 1) or Sn = (rTn - a)/(r - 1). These formulas help calculate the total of first n terms.

When three consecutive terms are unknown

When three consecutive terms are unknown, they can be represented as a/r, a, ar. This simplifies calculations compared to using a, ar, ar².