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
For which (x) will (x,24,96) be consecutive terms of a geometric progression?ExpertLevel 54What is the sum of the first (5) terms of the geometric progression (36,18,9,\frac{9}{2},\ldots)?ExpertLevel 54If (a_1=15) and (r=2), what will (a_4+a_6) be?ExpertLevel 54If \(a_1=27\) and \(r=\frac{2}{3}\), what will \(a_4\) be?ExpertLevel 54What will a_6 be in the geometric progression (3, -12, 48, -192, ...)?MediumLevel 54If (a_2=22) and (r=3), what is the value of (a_1+a_4)?ExpertLevel 54If (36,x,100) are consecutive terms of a positive geometric progression, what will (x) be?ExpertLevel 54If (a_1=4) and (a_4=500), and (r) is positive, what will (a_5) be?ExpertLevel 54If in a geometric progression a₂ + a₄ = 170 and r = 2, what is the first term a₁?HardLevel 54What is the tenth term of the geometric progression (2, 6, 18, 54, ...)?HardLevel 55If a geometric progression has (a=5) and (r=4), what is the value of (a_6)?ExpertLevel 55What is the ninth term of the geometric progression (1024,512,256,128,\ldots)?ExpertLevel 55If (a_n=7\cdot2^{n-1}), which term will be (1792)?ExpertLevel 55In a geometric progression, the first term is (4) and the fifth term is (324). If (r) is positive, what is (r)?ExpertLevel 55What is the general term of the geometric progression (6,24,96,384,\ldots)?ExpertLevel 55What is the sum of the first 7 terms of the geometric progression (3, 9, 27, 81, ...)?HardLevel 55If (12,x,108) are in geometric progression and (x>0), what is (x)?ExpertLevel 55What is the sum of the first (8) terms of the geometric progression (8,16,32,64,\ldots)?ExpertLevel 55In a geometric progression with all terms non-zero, which relation must hold for every interior term \(a_n\)?ExpertLevel 55What is the general term of the geometric progression (243,81,27,9,\ldots)?ExpertLevel 55