Last Updated: 3 May 2026Verified for JEE 2027
MathematicsJEE
Difference Between Arithmetic Progression (AP) and Geometric Progression (GP)
AP and GP are fundamental sequences in mathematics. In AP, consecutive terms differ by a constant; in GP, consecutive terms have a constant ratio.
Arithmetic Progression (AP) vs Geometric Progression (GP) — Comparison Table
| Aspect | Arithmetic Progression (AP) | Geometric Progression (GP) |
|---|---|---|
| Pattern | Common difference (d) | Common ratio (r) |
| nth term | a + (n-1)d | ar^(n-1) |
| Sum of n terms | n/2[2a+(n-1)d] | a(r^n-1)/(r-1) |
| Example | 2, 5, 8, 11 (d=3) | 2, 6, 18, 54 (r=3) |
| Mean | Arithmetic mean: (a+b)/2 | Geometric mean: √(ab) |
| Growth | Linear growth | Exponential growth |
Key Points to Remember
AM ≥ GM for positive numbers (AM-GM inequality)
Infinite GP sum = a/(1-r) when |r| < 1
If a, b, c are in AP: 2b = a + c
If a, b, c are in GP: b² = ac
Exam Relevance
This topic falls under Sequences and Series in Mathematics for JEE. Questions on the difference between arithmetic progression (ap) and geometric progression (gp) appear frequently in competitive exams, both as direct MCQs and as part of numerical/assertion-reason problems.
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