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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

If (a_n=256) in (1,4,16,64,\ldots), what is (n)?MediumLevel 53 In the geometric progression (2,6,18,54,\ldots), what is (a_3+a_4)?MediumLevel 53 If a geometric progression has a = 16 and r = 1/2, what is the sum of its first four terms?MediumLevel 53 What is the common ratio in the sequence (4,12,36,108,\ldots)?EasyLevel 57 What will be the next term of the geometric progression (7,14,28,56,\ldots)?EasyLevel 57 If a geometric progression has first term 5 and common ratio 3, what is the second term?EasyLevel 57 What is the common ratio in the sequence (125,25,5,1,\ldots)?EasyLevel 57 Is the sequence (2, 8, 32, 128, …) a geometric progression?EasyLevel 57 Why is the sequence (3, 6, 9, 12, …) not a geometric progression?EasyLevel 57 What is the first term in the geometric progression (9, 27, 81, 243, ...)?EasyLevel 57 What is the next term of the geometric progression (162,54,18,6,\ldots)?EasyLevel 57 What is the fifth term in the geometric progression (3,12,48,192,\ldots)?EasyLevel 57 If (5,,\Box,,45,135,\ldots) is a geometric progression what term fills the blank?EasyLevel 57 What is the general term of the geometric progression (2,8,32,128,\ldots)?EasyLevel 57 If (a_n=5^n) what is the value of (a_3)?EasyLevel 57 Which is the general term of the geometric progression (6,18,54,162,\ldots)?EasyLevel 57 If the first term of a geometric progression is 40 and the common ratio is 1/2, what is the second term?EasyLevel 57 Why is the sequence (1,3,6,10,\ldots) not a geometric progression?EasyLevel 57 What is the value of r in the geometric progression (10, 40, 160, 640, …)?EasyLevel 57 If (a=5) and (r=3) what is the fourth term of the geometric progression?EasyLevel 57