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
In the geometric progression (7,14,28,56,\ldots), which term is (224)?MediumLevel 53Which sequence is not a geometric progression?MediumLevel 53If a geometric progression has (a=6) and (r=2), what are the first four terms?MediumLevel 53What is the common ratio of the sequence (2,-6,18,-54,\ldots)?MediumLevel 53What is the next term in the geometric progression (4,12,36,\ldots)?MediumLevel 53If (3,x,27) are three consecutive positive terms of a geometric progression, what is (x)?MediumLevel 53What is the sum of the first (4) terms of the geometric progression (5,15,45,135,\ldots)?MediumLevel 53If a geometric progression has \(a_2=10\) and \(r=2\), what is \(a_1\)?MediumLevel 53If a geometric progression has (a_1=4) and (a_4=108), what is the common ratio?MediumLevel 53What is the (6)th term of the sequence \(\frac{1}{2},1,2,4,\ldots\)?MediumLevel 53What is the fifth term of the geometric progression (64,32,16,8,\ldots)?MediumLevel 53If \(a=3\) and \(r=5\), what is \(a_4\)?MediumLevel 53Which option has common ratio (\frac{1}{4})?MediumLevel 53In the geometric progression (1,3,9,27,\ldots), which term is (81)?MediumLevel 53If \(a_n=9\left(\frac{1}{3}\right)^{n-1}\), what is \(a_3\)?MediumLevel 53If \((2,6,x,54)\) is a geometric progression, what is \(x\)?MediumLevel 53Which sequence has a negative common ratio?MediumLevel 53What is the sum of the first (4) terms of the geometric progression (10,20,40,80,\ldots)?MediumLevel 53Which condition is necessary for a sequence to be a geometric progression (GP)?MediumLevel 53What is the (n)th term of the sequence (6,18,54,162,\ldots)?MediumLevel 53