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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

Why is the sequence (1,4,9,16,\ldots) not a geometric progression?EasyLevel 56 What is the value of \(r\) in the geometric progression \((4,12,36,108,\ldots)\)?EasyLevel 56 If \(a=6\) and \(r=2\), what is the fourth term of the geometric progression?EasyLevel 56 What is the fifth term in the geometric progression (100,50,25,\frac{25}{2},\ldots)?EasyLevel 56 In the geometric progression (1,2,4,8,\ldots), which term is (16)?EasyLevel 56 If \(a_n=3\cdot2^{n-1}\), what first three terms does it give?EasyLevel 56 What is the general term of the geometric progression (8,24,72,216,\ldots)?EasyLevel 56 If (2,10,50,\Box,\ldots) is a geometric progression, what term fills the blank?EasyLevel 56 What is the common ratio in the geometric progression (32,16,8,4,\ldots)?EasyLevel 56 What will be the sixth term in the geometric progression (6,18,54,162,\ldots)?EasyLevel 56 Is (10,20,40,80,\ldots) a geometric progression?EasyLevel 56 If (a=2) and (r=5), what are the first four terms?EasyLevel 56 Which is the general term of the geometric progression (27,9,3,1,\ldots)?EasyLevel 56 If a_n = 16(1/2)^(n-1), what is the value of a_4?EasyLevel 56 What are (a) and (r) in the geometric progression (1,5,25,125,\ldots)?EasyLevel 56 If a geometric progression has \(a=7\) and \(r=2\), what is the fifth term?EasyLevel 56 In the sequence (4,8,16,32,\ldots), which term is (64)?EasyLevel 56 Which of the following sequences is an example of a geometric progression?EasyLevel 56 What is the next term of the geometric progression (9,18,36,72,\ldots)?EasyLevel 56 In a geometric progression, how is each term related to the term immediately preceding it?EasyLevel 56