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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 a geometric progression with (a=3) and (a_6=96), if (r) is positive, what is (r)?ExpertLevel 55 In the geometric progression (5,20,80,320,\ldots), which term is (5120)?ExpertLevel 55 If \(a=160\) and \(r=\frac{1}{2}\), what is the value of \(a_6\)?ExpertLevel 55 If the sum of the first 5 terms of a geometric progression is 363, with a = 3 and r = 3, which statement is correct?MediumLevel 55 What is the sum of the first 6 terms of the geometric progression 1, 4, 16, 64, …?MediumLevel 55 In a geometric progression (a_4=48) and (a_8=768). If (r) is positive, what is (r)?ExpertLevel 55 Which of the following sequences is not a geometric progression?ExpertLevel 55 What is (a_9\div a_5) for the geometric progression (4,12,36,108,\ldots)?ExpertLevel 55 If (a_n=9\cdot2^{n-1}), what is the sum of the first (8) terms?ExpertLevel 55 Which term of the geometric progression (3,15,75,\ldots) is (9375)?ExpertLevel 55 If (a_2=18) and (a_6=1458), what is the positive value of (r)?ExpertLevel 55 If (a=6) and (a_7=384), and (r) is positive, what is (r)?ExpertLevel 55 What is the sum of the first (7) terms of the geometric progression (6,18,54,\ldots)?ExpertLevel 55 In a geometric progression (a_3=50) and (a_6=6250). If (r) is positive, what is (a_1)?ExpertLevel 55 If the fifth term of the geometric progression (x,,5x,,25x,\ldots) is (3125), what is (x)?ExpertLevel 55 How many terms are there up to (4096) in the geometric progression (4,16,64,\ldots)?ExpertLevel 55 If the first (4) terms of a geometric progression are (7,21,63,189), what is (S_4)?ExpertLevel 55 Which term of the geometric progression (2,8,32,\ldots) is (8192)?ExpertLevel 55 If (a_1=9) and (r=-2), what is (a_8)?ExpertLevel 55 What is the sum of the first (4) terms of the geometric progression (5,30,180,1080,\ldots)?ExpertLevel 55