Maths > Sequence and Series > 5.0 Relation among A.M., G.M. and H.M.
Sequence and Series
1.0 Introduction
2.0 Arithmetic Sequence or Arithmetic Progression (A.P.)
3.0 Geometric Sequence or Geometric Progression (G.P.)
4.0 Harmonic Sequence or Harmonic Progression (H.P.)
5.0 Relation among A.M., G.M. and H.M.
6.0 $\Sigma $, Sigma Notation
7.0 Arithmetico-Geometric Series (A.G.S.)
8.0 Miscellaneous Series
5.1 Recognization of A.P., G.P. and H.P.
- If $a$, $b$ and $c$ are three successive terms of a sequence, then
- If $$\frac{{a - b}}{{b - c}} = \frac{a}{a} = 1$$ Then $a$,$b$,$c$ are in A.P.
- If $$\frac{{a - b}}{{b - c}} = \frac{a}{b}$$ Then $a$,$b$,$c$ are in G.P.
- If $$\frac{{a - b}}{{b - c}} = \frac{a}{c}$$ Then $a$,$b$,$c$ are in H.P.
