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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

Which sequence is formed by a multiplication rule, not an addition rule?MediumLevel 41 What is the 7th term of (4, 12, 36, 108, ...)?MediumLevel 42 In the sequence \((81,27,9,3,\ldots)\), each term is \(\frac{1}{3}\) of the previous term. What is the sixth term?MediumLevel 44 In the sequence 3, 6, 12, 24, ..., which is the first term greater than 500?MediumLevel 43 In the sequence 5, 10, 20, 40, ..., which term is 5120?MediumLevel 43 What is the common ratio in the sequence (2, 6, 18, 54, ...)?EasyLevel 56 What will be the next term of the geometric progression (5,10,20,40,\ldots)?EasyLevel 56 If a geometric progression has first term (4) and common ratio (2), what is the second term?EasyLevel 56 What is the common ratio in the sequence (81,27,9,3,\ldots)?EasyLevel 56 Is the sequence (3, 6, 12, 24, ...) a geometric progression?EasyLevel 56 Why is the sequence (2, 4, 6, 8, ...) not a geometric progression?EasyLevel 56 What is the first term in the geometric progression (7, 21, 63, 189, ...)?EasyLevel 56 If (a=3) and (r=4), what is the third term of the geometric progression?EasyLevel 56 What is the next term of the geometric progression (64,32,16,8,\ldots)?EasyLevel 56 What is the fifth term in the geometric progression (2,6,18,54,\ldots)?EasyLevel 56 If (4,,\Box,,36,108,\ldots) is a geometric progression, what term fills the blank?EasyLevel 56 What is the general term of the geometric progression (3,9,27,81,\ldots)?EasyLevel 56 If (a_n=2^n), what is the value of (a_5)?EasyLevel 56 Which is the general term of the geometric progression (5,15,45,135,\ldots)?EasyLevel 56 If the first term of a geometric progression is 18 and the common ratio is 1/3, what is the second term?EasyLevel 56