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 (3,15,75,375,\ldots), what is the greatest term less than (10000)?ExpertLevel 54If (a_1=9) and (r=3), what will (a_4+a_5) be?ExpertLevel 54If (12,36,108,\ldots) is a geometric progression, what is the value of (a_6-a_4)?ExpertLevel 54In a geometric progression, a_3 = 18 and a_5 = 288. For positive r, what will a_7 be?HardLevel 54If \(a_n=125\left(\frac{1}{5}\right)^{n-1}\), what is \(a_2+a_4\)?ExpertLevel 54If a₁ = 10 and r = −2, what will be the sum of the first 5 terms?MediumLevel 54If (a_4=54) and (a_8=4374), and (r) is positive, what is (r)?ExpertLevel 54Which geometric progression has common ratio (-\frac{1}{4})?ExpertLevel 54If a geometric progression has (a_2=10) and (a_4=250), what will (a_1+a_5) be for positive (r)?ExpertLevel 54If \(a_n=8\cdot3^{n-1}\), what will (n) be for \(a_n=1944\)?ExpertLevel 54The consecutive terms of a geometric progression are (x, 5x, 125). What is the positive x?MediumLevel 54If a₁ = 10 and r = 3, what is a₆ − a₄?MediumLevel 54Which statement correctly describes the geometric progression (40,20,10,5,\ldots)?ExpertLevel 54If \(a_3=45\) and \(r=\frac{1}{3}\), what will \(a_6\) be?ExpertLevel 54In the geometric progression (11,22,44,\ldots), what is the greatest term less than (800)?ExpertLevel 54If (a_2=15) and (a_6=1215), and the ratio is positive, what will (a_7) be?ExpertLevel 54If (a_1=3) and (r=4), what will be the product of the first (4) terms?ExpertLevel 54In a geometric progression, (a_1=10) and (a_4=270). What will be the positive (r)?ExpertLevel 54If (a_n=5\cdot4^{n-1}), what is the value of (\frac{a_7}{a_4})?ExpertLevel 54If a_3 = 40 and a_5 = 360, and r is positive, what will a_7 be?MediumLevel 54