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 three non-zero numbers \(x, y, z\), in this order, are consecutive terms of a geometric progression, which relation must hold?HardLevel 55What is the sixth term of the geometric progression (625,125,25,5,\ldots)?HardLevel 55If (a_n=6\cdot2^{n-1}), which term will be (1536)?HardLevel 55In a geometric progression, the first term is (5) and the seventh term is (320). If (r) is positive, what is (r)?HardLevel 55What is the general term of the geometric progression (12,48,192,768,\ldots)?HardLevel 55What is the sum of the first 6 terms of the geometric progression (3, 9, 27, 81, ...)?MediumLevel 55If (12,x,75) are in geometric progression and (x>0), what is (x)?HardLevel 55What is the sum of the first (5) terms of the geometric progression (4,20,100,500,\ldots)?HardLevel 55Which condition is necessary and sufficient for a sequence with non-zero terms to be a geometric progression?HardLevel 55What is the general term of the geometric progression \(100,50,25,\frac{25}{2},\ldots\)?HardLevel 55For a geometric progression with (a=9) and (a_5=2304), if (r) is positive, what is (r)?HardLevel 55In the geometric progression (6,18,54,162,\ldots), which term is (4374)?HardLevel 55If \(a=192\) and \(r=\frac{1}{2}\), what is the value of \(a_8\)?HardLevel 55If the sum of the first 4 terms of a geometric progression is 340 with a = 4 and r = 4, what is the statement?MediumLevel 55What is the sum of the first 7 terms of the geometric progression (2,8,32,128,...)?MediumLevel 55In a geometric progression (a_2=14) and (a_6=224). If (r) is positive, what is (r)?HardLevel 55If \(x, y, z\) are three consecutive terms of a geometric progression, which of the following relations is always true?HardLevel 55What is (a_9\div a_4) for the geometric progression (8,16,32,64,\ldots)?HardLevel 55If (a_n=5\cdot3^{n-1}), what is the sum of the first (6) terms?HardLevel 55Which term of the geometric progression (4,12,36,\ldots) is (972)?HardLevel 55