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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

What is the next term in the geometric progression (72,24,8,\ldots)?MediumLevel 54 If (a_n=6\cdot3^{n-1}), which sequence does it form?MediumLevel 54 If (x,18,54) are consecutive terms of a geometric progression, what is (x)?MediumLevel 54 What is the (5)th term of the geometric progression (5,20,80,\ldots)?MediumLevel 54 Which sequence has common ratio (4)?MediumLevel 54 If \(a_1=\frac{5}{8}\) and \(r=2\), what is \(a_5\)?MediumLevel 54 What is the sum of the first (5) terms of the geometric progression (3,6,12,24,\ldots)?MediumLevel 54 If a1 = 4 and the common ratio r = -3, what are the first four terms?MediumLevel 54 For which (x) will (9,x,49) be consecutive terms of a positive geometric progression?MediumLevel 54 What is the (n)th term of the sequence (11,33,99,297,\ldots)?MediumLevel 54 If (a_2=30) and (a_5=810), and the ratio is positive, what is (r)?MediumLevel 54 In the geometric progression (4, 16, 64, ...), what is a₅?MediumLevel 54 If a geometric progression has (a_1=3) and (a_3=75), what is the positive (r)?MediumLevel 54 Which statement is correct for (18,6,2,\frac{2}{3},\ldots)?MediumLevel 54 If (a_n=512) in (2,8,32,128,\ldots), what is (n)?MediumLevel 54 In the geometric progression (4,12,36,108,\ldots), what is (a_2+a_4)?MediumLevel 54 If a geometric progression has first term a = 24 and common ratio r = 1/2, what is the sum of its first four terms?MediumLevel 54 If a geometric progression has (a_2=18) and (r=2), what will (a_5) be?MediumLevel 54 For which (x) will (5,x,45) be consecutive terms of a positive geometric progression?MediumLevel 54 What is the average of the first (4) terms of the geometric progression (15,30,60,120,\ldots)?MediumLevel 54