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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=1) and (r=2), what will be the sum of the first (6) terms?MediumLevel 53 Which value of (x) makes (4,20,x) a geometric progression?MediumLevel 53 In the sequence (2,8,32,128,\ldots), which term is (512)?MediumLevel 53 If a geometric progression has (a_2=18) and (a_4=162), what is (r)?MediumLevel 53 What is the fifth term of the geometric progression \((1,-2,4,-8,\ldots)\)?MediumLevel 53 Which option has the first four terms of a geometric progression with (a=9) and (r=3)?MediumLevel 53 If (5,15,45,\ldots) is a geometric progression, what is the product of the first three terms?MediumLevel 53 What is the next term in the geometric progression (100,50,25,\ldots)?MediumLevel 53 If \(a_n=4\cdot2^{n-1}\), which sequence does it form?MediumLevel 53 If (x,12,36) are consecutive terms of a geometric progression, what is (x)?MediumLevel 53 What is the (6)th term of the geometric progression (8,24,72,\ldots)?MediumLevel 53 Which sequence has common ratio (5)?MediumLevel 53 If \(a_1= \frac{3}{4}\) and \(r=2\), what is \(a_4\)?MediumLevel 53 What is the sum of the first (5) terms of the geometric progression (2,4,8,16,\ldots)?MediumLevel 53 For which (x) will (8,x,18) be consecutive terms of a positive geometric progression?MediumLevel 53 What is the (n)th term of the sequence (7,21,63,189,\ldots)?MediumLevel 53 If (a_2=24) and (a_5=192), and the ratio is positive, what is (r)?MediumLevel 53 In the geometric progression (3, 12, 48, …), what is a₅?MediumLevel 53 If a geometric progression has (a_1=2) and (a_3=50), what is the positive (r)?MediumLevel 53 Which statement is correct for (12,6,3,\frac{3}{2},\ldots)?MediumLevel 53