Mathematics
Geometric Progression
गुणोत्तर श्रेणी
In this Class 9 Mathematics topic from Sequences and Progressions, students explore sequences in which each term is obtained by multiplying the preceding term by a fixed number. They learn to identify the common ratio, distinguish a geometric progression from other patterns, write its terms, and use the general term to find a specific position in the sequence. Examples help connect the idea with repeated growth, decrease, and everyday numerical patterns.
Practice questions
The consecutive terms of a geometric progression are x, 3x, and 27. What is the positive value of x?MediumLevel 53If a₁ = 6 and r = 3, what is a₆ − a₄?MediumLevel 53Which statement correctly describes the geometric progression (18,6,2,\frac{2}{3},\ldots)?ExpertLevel 53If \(a_2=24\) and \(r=\frac{1}{2}\), what will be \(a_5\)?ExpertLevel 53In the geometric progression (2,10,50,\ldots), what is the greatest term less than (6000)?ExpertLevel 53If all terms of a sequence are non-zero, which of the following conditions is sufficient to identify the sequence as a geometric progression?ExpertLevel 53If a₁ = 1 and r = 4, what is the product of the first 4 terms of the geometric progression?MediumLevel 53In the geometric progression (a,ar,ar^2,\ldots), (a_1=9) and (a_4=72). What will be the positive (r)?ExpertLevel 53If (a_n=7\cdot3^{n-1}), what is the value of (\frac{a_5}{a_3})?ExpertLevel 53If a₂ = 20 and a₄ = 80 in a geometric progression, and r is positive, what is a₆?MediumLevel 53For which (x) will (x,12,48) be consecutive terms of a geometric progression?ExpertLevel 53What is the sum of the first (5) terms of the geometric progression (12,6,3,\frac{3}{2},\ldots)?ExpertLevel 53If (a_1=11) and (r=3), what will (a_3+a_5) be?ExpertLevel 53If \(a_1=8\) and \(r=\frac{3}{2}\), what will \(a_4\) be?ExpertLevel 53What is a₇ in the geometric progression (1, −3, 9, −27, …)?MediumLevel 53If (a_2=14) and (r=5), what is the value of (a_1+a_3)?ExpertLevel 53If (16,x,81) are consecutive terms of a positive geometric progression, what will (x) be?ExpertLevel 53Which option can form a geometric progression?ExpertLevel 53If (a_1=5) and (a_4=625), and (r) is positive, what will (a_5) be?ExpertLevel 53What is the twelfth term of the geometric progression (7,14,28,56,...)?MediumLevel 55