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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

If (a_4=162) and (r=3), what is the value of (a_9)?ExpertLevel 55 In the geometric progression (486,162,54,\ldots), which term is (2)?ExpertLevel 55 If a = 8, r = 4, and S₄ = 680, which statement is correct?MediumLevel 55 What is the value of a₅ + a₆ for the geometric progression 3, 12, 48, …?MediumLevel 55 If \(a_n=405\left(\frac{1}{3}\right)^{n-1}\), which term will be equal to (5)?ExpertLevel 55 What is the sum of the first (9) terms of the geometric progression (10,20,40,\ldots)?ExpertLevel 55 In a geometric progression with non-zero terms, which of the following relations is always true for three consecutive terms?ExpertLevel 55 If all terms of a geometric progression are positive and its common ratio is less than 1, which statement about its terms is correct?ExpertLevel 55 If \(a=96\) and \(r=\frac{1}{2}\), what is the sum of the first \(6\) terms?ExpertLevel 55 In a geometric progression, (a_2=20) and (a_5=2500). What is (a_1)?ExpertLevel 55 If aₙ = 6 × 5ⁿ⁻¹, what is the value of a₄ + a₅?MediumLevel 55 In the geometric progression (15,30,60,\ldots), if (a_n=3840), what is (n)?ExpertLevel 55 If (a_1=10) and (a_4=270), and (r) is positive, what is (a_5)?ExpertLevel 55 What is the sum of the first (10) terms of the geometric progression (12,24,48,\ldots)?ExpertLevel 55 If (a_8=1280) and (a=10), and (r) is positive, what is (r)?ExpertLevel 55 In the geometric progression (120,40,\frac{40}{3},\frac{40}{9},\ldots), which term is (\frac{40}{81})?ExpertLevel 55 If (a=4) and (r=6), what is the value of (a_4+a_5)?ExpertLevel 55 How many terms of the geometric progression (5,15,45,\ldots) have sum (1820)?ExpertLevel 55 If \(x, y, z\) are three consecutive terms of a geometric progression and \(x\neq0\) and \(y\neq0\), which is the necessary and sufficient condition for them?ExpertLevel 55 What is the sixth term of the geometric progression (64, 32, 16, ...)?MediumLevel 56