# Geometric Progressions Questions and Answers

# Geometric Progressions Questions

## Definition of G.P.

**A geometric progression is a kind of order that includes an organized and immeasurable assortment of real numbers, wherein every term is acquired by multiplying its previous term through a constant value. Furthermore, the progression of the wat: a, ar, ar², ar³and so on is known as a GP.The foremost term is denoted as = aThe common ratio is denoted as = r **

**Formula or Rule for solving G.P.**

- The nth term, Tn = arn– 1
- Sum to n terms,

Sn =(a (1-r^{n}))/((1-r)), When r < 1 and Sn =(a (r^{(n-1)}))/((r-1)), When r > 1 - If x, y, z are in GP, then y is the geometric mean between x and z. In this case,

y = √xz - The sum of an infinite GP a, ar, ar
^{2}and so on is a/(1-r) - If ‘a’ is known as the foremost term, and ‘r’ is the common ratio of a limited G.P. which consists of m terms, then from the end the nth term will be = ar
^{(m-n)}. - If the last term is denoted as ‘l’ and common ratio as ‘r’, then from the end the nth of the G.P. will be calculated as: l/(r
^{(n-l)}).