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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 geometric progression has (a_1=7) and (r=5) what is (a_3)?EasyLevel 58 What is the tenth term of the geometric progression (3,6,12,24,\ldots)?EasyLevel 58 If \(a_n=2\cdot5^{n-1}\) what is the value of \(a_4\)?EasyLevel 58 What is the general term of the geometric progression \(60,30,15,\frac{15}{2},\ldots\)?EasyLevel 58 If (10,,x,,90) is a geometric progression what is the positive value of (x)?EasyLevel 58 What will be the fifth term in the geometric progression (18,54,162,486,\ldots)?EasyLevel 58 Which geometric progression has first term 8 and common ratio 3?EasyLevel 58 If (a=12) and (r=2) what will be the sixth term of the geometric progression?EasyLevel 58 If a geometric progression has (a_2=15) and (r=3) what is (a_3)?EasyLevel 58 If a geometric progression has first term (6) and common ratio (4), what is the third term?MediumLevel 55 What is the common ratio of the sequence (125,25,5,1,\ldots)?MediumLevel 55 If \(a_n=5\cdot3^{n-1}\), what is the value of \(a_5\)?MediumLevel 55 In the geometric progression 8, 16, 32, 64, ..., which term is 256?MediumLevel 55 If a geometric progression has (a=10) and (r=2), what are the first four terms?MediumLevel 55 What is the common ratio of the sequence (7,-14,28,-56,\ldots)?MediumLevel 55 What is the next term in the geometric progression (6,30,150,\ldots)?MediumLevel 55 If (9,x,81) are consecutive positive terms of a geometric progression, what is (x)?MediumLevel 55 What is the sum of the first (4) terms of the geometric progression (8,24,72,216,\ldots)?MediumLevel 55 If a geometric progression has (a_2=28) and (r=4), what is (a_1)?MediumLevel 55 If a geometric progression has (a_1=3) and (a_4=81), and the ratio is positive, what is (r)?MediumLevel 55