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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

What is the common ratio in the sequence (6,18,54,162,\ldots)?EasyLevel 58 What will be the next term of the geometric progression (4,16,64,256,\ldots)?EasyLevel 58 If a geometric progression has first term 7 and common ratio 4, what is its second term?EasyLevel 58 What is the common ratio in the sequence (243,81,27,9,\ldots)?EasyLevel 58 Is the sequence (5, 25, 125, 625, ...) a geometric progression?EasyLevel 58 Why is the sequence (2,6,12,20,\ldots) not a geometric progression?EasyLevel 58 What is the first term in the geometric progression (12, 36, 108, 324, ...)?EasyLevel 58 If \(a=2\) and \(r=6\) what is the third term of the geometric progression?EasyLevel 58 What is the next term of the geometric progression (128,64,32,16,\ldots)?EasyLevel 58 What is the fifth term in the geometric progression (4,12,36,108,\ldots)?EasyLevel 58 If (6,,\Box,,54,162,\ldots) is a geometric progression what term fills the blank?EasyLevel 58 What is the general term of the geometric progression (5,20,80,320,\ldots)?EasyLevel 58 If (a_n=6^n) what is the value of (a_2)?EasyLevel 58 Which is the general term of the geometric progression (8,40,200,1000,\ldots)?EasyLevel 58 If the first term of a geometric progression is 54 and the common ratio is 1/3, what is the second term?EasyLevel 58 Why is the sequence (2,5,10,17,\ldots) not a geometric progression?EasyLevel 58 What is the value of r in the geometric progression 15, 45, 135, 405, ...?EasyLevel 58 Which of the following sequences is a geometric progression (GP)?EasyLevel 58 What is the fifth term in the geometric progression (144,72,36,18,\ldots)?EasyLevel 58 In the geometric progression (5,15,45,135,\ldots) which term is (405)?EasyLevel 58