If a, b, c, d Are in G.P. — Relationship Between Terms
When a b c d are in G.P. (geometric progression), the terms follow a constant ratio. This idea is frequently used in sequence and series problems in Class 11 and Class 12 mathematics.
Definition of G.P.
A sequence a, b, c, d is in geometric progression if the ratio of consecutive terms is the same.
That is:
b/a = c/b = d/c = r
where r is the common ratio.
Relationships Among Terms
From the definition, we get:
- b = ar
- c = ar²
- d = ar³
Two useful relations derived from these are:
b² = ac
c² = bd
These identities are often used to simplify problems involving geometric progression and to prove algebraic relationships.
If a, b, c, d Are in G.P. — Relationship Between Terms
Keywords
a b c d are in G.P., geometric progression definition, common ratio, b² = ac, c² = bd, sequence and series, Class 11 math, Class 12 math, exam preparation, algebra, progression formulas, math notes, aklearningnepal
Tags
geometric progression, sequence and series, a b c d, common ratio, Class 11, Class 12, math notes, exam question, GP relations, algebra, aklearningnepal, education, If a, b, c, d Are in G.P. — Relationship Between Terms
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If a, b, c, d Are in G.P. — Relationship Between Terms