CAT Quant · Chapter Test
Geometric Progression — 25-Question Test
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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
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