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=7\cdot2^{n-1}) what is the common ratio of this geometric progression?EasyLevel 57What is (a_5) of the geometric progression (14,42,126,378,\ldots)?EasyLevel 57If a geometric progression has \(a_1=5\) and \(r=4\) what is \(a_3\)?EasyLevel 57Which sequence has common ratio (\frac{1}{3})?EasyLevel 57What is the tenth term of the geometric progression (4,8,16,32,\ldots)?EasyLevel 57If (a_n=4^n) what is the value of (a_3)?EasyLevel 57What is the general term of the geometric progression \(36,18,9,\frac{9}{2},\ldots\)?EasyLevel 57If (8,,x,,72) is a geometric progression what is the positive value of (x)?EasyLevel 57What will be the fifth term in the geometric progression (12,48,192,768,\ldots)?EasyLevel 57Which geometric progression has first term 6 and common ratio 4?EasyLevel 57Which of the following sequences is a geometric progression?EasyLevel 57What is the common ratio in the sequence (5,15,45,135,\ldots)?MediumLevel 54If a geometric progression has first term (4) and common ratio (5), what is the third term?MediumLevel 54What is the common ratio of the sequence (96,48,24,12,\ldots)?MediumLevel 54If \(a_n=3\cdot2^{n-1}\), what is the value of \(a_6\)?MediumLevel 54In the geometric progression (9,27,81,243,\ldots), which term is (729)?MediumLevel 54If a geometric progression has (a=8) and (r=3), what are the first four terms?MediumLevel 54What is the common ratio of the sequence (4,-12,36,-108,\ldots)?MediumLevel 54What is the next term in the geometric progression (2,10,50,\ldots)?MediumLevel 54If (4,x,64) are consecutive positive terms of a geometric progression, what is (x)?MediumLevel 54