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 = a
The 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-rn))/((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, ar2 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)).