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
All terms of a sequence are non-zero. Which of the following conditions, if true for every suitable n, confirms that the sequence is a geometric progression?ExpertLevel 54What is the seventh term of the geometric progression (8, -16, 32, -64, ...)?MediumLevel 54If (6,x,150) are consecutive terms of a positive geometric progression, what is the value of (x)?ExpertLevel 54If (a_1=7) and (a_5=1792), what will be the positive common ratio?ExpertLevel 54If \(p, q, r\) are three consecutive non-zero terms of a geometric progression, which of the following relations must be true?ExpertLevel 54Which sequence has both (a_3=45) and (a_6=1215)?ExpertLevel 54If \(a_n=4\cdot3^{n-1}\), what will be the value of \(a_4+a_6\)?ExpertLevel 54In the geometric progression (384,192,96,48,\ldots), which term is (6)?ExpertLevel 54If (a_3=36) and (a_7=576), and the ratio is positive, what will (a_1) be?ExpertLevel 54If (x+2,3x,6x+4) are consecutive positive terms of a geometric progression, what is (x)?ExpertLevel 54In the geometric progression (9,18,36,\ldots), what is the greatest term less than (600)?ExpertLevel 54If in a geometric progression a_2 + a_4 = 90 and r = 3, what will a_1 be?MediumLevel 54Which geometric progression has (a_1=32) and (a_5=2)?ExpertLevel 54If (a_1=4) and the sum of the first (5) terms is (484), and (r) is a positive integer, what is (r)?ExpertLevel 54In the geometric progression (5,-20,80,-320,\ldots), what is (a_5+a_3)?ExpertLevel 54If \(a_n=96\left(\frac{1}{2}\right)^{n-1}\), what is the value of \(a_3+a_6\)?ExpertLevel 54In a geometric progression, a_2 = 32 and a_6 = 8192. For positive r, what will a_1 be?HardLevel 54If (5, x, 80, y) is a geometric progression and all terms are positive, what will y be?MediumLevel 54Which sequence has a_4 = 96 and r = 2?EasyLevel 54If \(a_1=\frac{7}{2}\) and \(r=4\), what will \(a_4\) be?ExpertLevel 54