IIT JEE Geometric Mean | JEE Geometric Mean of A and B

Geometric Mean between two numbers

If three numbers are in G.P. then middle one is said to be geometric mean (GM) of two others.
Let, G be the geometric mean between two number a and b
So, a G b are in G.P.
G/a = b/G.
or,    G2 = ab
∴  G =√ab
Similarly we can find two geometric means between two given numbers a and b.
Let a, G1, G2, b are in G.P.
tn = a rn–1
or b/a = r3
r =(b/a)1/3
G1 = ar2 = a (b/a)1/3 = a1/3 b2/3

Geometric Mean(s)

  • If three terms are in G.P., then the middle term is called the geometric mean (G.M.) between the two. So if a, b, c are in G.P., then b = √ac is the geometric mean of a and c.

  • If a1, a2, ……, an are non-zero positive numbers, then their G.M.(G) is given by G = (a1a2a3, ……, an)1/n. If G1, G2, …… Gn are n geometric means between and a and b then a, G1, G2, ……, Gn b will be a G.P. Here b = arn+1.

⇒ r = n+1√b/a  G1 = an+1√b/a, G2 = a(n+1√b/a)2,…, Gn = a(n+1√b/a)n.

To read more, Buy study materials of Sequences and Series comprising study notes, revision notes, video lectures, previous year solved questions etc. Also browse for more study materials on Mathematics here.


Upto 50% Scholarship on Live Classes

Course Features

  • Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution