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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 (x,20,100) are consecutive terms of a geometric progression, what is (x)?MediumLevel 55 What is the (6)th term of the geometric progression (6,18,54,\ldots)?MediumLevel 55 Which sequence has common ratio (6)?MediumLevel 55 If \(a_1=\frac{7}{4}\) and \(r=2\), what is \(a_4\)?MediumLevel 55 What is the sum of the first 6 terms of the geometric progression (4, 8, 16, 32, …)?MediumLevel 55 If \(a_1=5\) and \(r=-2\), what are the first four terms?MediumLevel 55 For which (x) will (16,x,81) be consecutive terms of a positive geometric progression?MediumLevel 55 What is the (n)th term of the sequence (13,39,117,351,\ldots)?MediumLevel 55 If \(a_2=40\) and \(a_5=320\), and the ratio is positive, what is \(r\)?MediumLevel 55 In the geometric progression (5, 25, 125, ...), what is a₄?MediumLevel 55 If a geometric progression has (a_1=6) and (a_3=150), what is the positive (r)?MediumLevel 55 Which statement is correct for (24,12,6,3,\ldots)?MediumLevel 55 If (a_n=768) in (3,12,48,192,\ldots), what is (n)?MediumLevel 55 In the geometric progression (6,18,54,162,\ldots), what is (a_2+a_4)?MediumLevel 55 If a geometric progression has first term a = 32 and common ratio r = 1/2, what is the sum of the first four terms?MediumLevel 55 If a geometric progression has (a_3=20) and (r=3), what will (a_6) be?MediumLevel 55 For which (x) will (12,x,75) be consecutive terms of a positive geometric progression?MediumLevel 55 What is the next term in the geometric progression (48,-24,12,-6,\ldots)?MediumLevel 55 If \(a_n=7\cdot2^{n-1}\), what is the value of \(a_4+a_5\)?MediumLevel 55 What is the twelfth term of the geometric progression \(3,6,12,24,\ldots\)?HardLevel 54