Module 2 · Algebra
Chapter 25: Geometric Progression
Algebra
3 topics
What this chapter covers
The 3 topics below make up Geometric Progression on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
📚 Study this chapter
Notes, worked examples and hint-guided practice for every topic.
Start learning →
🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
Practice by topic →
📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
Take chapter test →
Formula Reference Sheet
This chapter
Core GP formulas
| nth term | a_n = a·r^(n−1) |
|---|---|
| Sum of n terms (r ≠ 1) | S_n = a(r^n − 1)/(r − 1) |
| Sum of n terms (|r| < 1 form) | S_n = a(1 − r^n)/(1 − r) |
| Infinite sum (|r| < 1) | S_∞ = a/(1 − r) |
| Geometric mean of a and b | GM = √(ab) |
CAT power-tools
| Three terms in GP | a/r, a, ar (product = a³) |
|---|---|
| Ratio of two terms | a_m / a_n = r^(m − n) |
| n GMs between a and b | common ratio r = (b/a)^(1/(n+1)) |
| Sum × (r − 1) | S_n(r − 1) = a(r^n − 1) |
| Each term squared | a², a²r², a²r⁴, ... is a GP with ratio r² |
CAT reference
🖩 Graphing Calculator