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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

In the geometric progression (3,6,12,\ldots), what is the greatest term less than (100)?ExpertLevel 53 If \(a_2=10\) and \(a_6=160\) in a geometric progression, and the common ratio is positive, what is \(a_1\)?MediumLevel 53 Which geometric progression has (a_1=12) and (a_4=\frac{3}{2})?ExpertLevel 53 If (a_1=2) and the sum of the first (5) terms is (62), and (r) is a positive integer, what is (r)?ExpertLevel 53 In the geometric progression (9,-27,81,-243,\ldots), what is (a_6+a_4)?ExpertLevel 53 If \(a_n=48\left(\frac{1}{2}\right)^{n-1}\), what is the value of \(a_3+a_5\)?ExpertLevel 53 In a geometric progression, a₂ = 15 and a₅ = 405. If r is positive, what is a₁?MediumLevel 53 If (2,x,18,y) is a geometric progression and all terms are positive, what will (y) be?ExpertLevel 53 Which sequence has a₃ = 50 and common ratio r = 5?EasyLevel 53 If \(a_1=\frac{3}{2}\) and \(r=4\), what will be \(a_5\)?ExpertLevel 53 In the geometric progression (1,3,9,27,\ldots), what is the greatest term less than (1000)?ExpertLevel 53 If three non-zero numbers \(a, b, c\), in this order, are consecutive terms of a geometric progression, which of the following condition is necessary and sufficient?ExpertLevel 53 If (6,18,54,\ldots) is a geometric progression, what is the value of (a_5-a_3)?ExpertLevel 53 In the geometric progression (a,ar,ar^2,\ldots), (a_2=8) and (a_4=128). What will be (a_6)?ExpertLevel 53 If \(a_n=81\left(\frac{1}{3}\right)^{n-1}\), what is \(a_2+a_5\)?ExpertLevel 53 If a₁ = 4 and r = −2 in a geometric progression, what is the sum of the first 5 terms?MediumLevel 53 If (a_3=45) and (a_7=3645), and (r) is positive, what is (r)?ExpertLevel 53 Which geometric progression has common ratio (-\frac{1}{2})?ExpertLevel 53 If a geometric progression has (a_2=6) and (a_4=54), what will be the value of (a_1+a_5)?ExpertLevel 53 If \(a_n=5\cdot2^{n-1}\), what will (n) be for \(a_n=320\)?ExpertLevel 53