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 fifth term in the geometric progression (200,100,50,25,\ldots)?EasyLevel 56If \((x,3x,9x,\ldots)\) is a geometric progression, what is the common ratio?EasyLevel 56What is the common ratio in the geometric progression (5,5,5,5,\ldots)?EasyLevel 56If (a=11) and (r=1), what are the first three terms?EasyLevel 56What is the missing term in the geometric progression (3,\Box,27,81,\ldots)?EasyLevel 56If (a_n=4\cdot2^{n-1}), what is the common ratio of this geometric progression?EasyLevel 56What is (a_5) of the geometric progression (12,36,108,324,\ldots)?EasyLevel 56Which of the following properties identifies a geometric progression?EasyLevel 56Which sequence has common ratio (\frac{1}{4})?EasyLevel 56What is the tenth term of the geometric progression (2,4,8,16,\ldots)?EasyLevel 56If (a_n=3^n), what is the value of (a_4)?EasyLevel 56What is the general term of the geometric progression \(20,10,5,\frac{5}{2},\ldots\)?EasyLevel 56If (6,,x,,54) is a geometric progression, what is the positive value of (x)?EasyLevel 56What will be the fifth term in the geometric progression (15,45,135,405,\ldots)?EasyLevel 56Which geometric progression has first term 4 and common ratio 3?EasyLevel 56What is the common ratio in the sequence \((3,6,12,24,\ldots)\)?MediumLevel 53If a geometric progression has first term (5) and common ratio (3), what is the fourth term?MediumLevel 53Which sequence is a geometric progression?MediumLevel 53What is the common ratio of the sequence (81,27,9,3,\ldots)?MediumLevel 53If \(a_n=2\cdot4^{n-1}\), what is the value of \(a_5\)?MediumLevel 53