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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 a geometric progression (a_2=18) and (a_5=486). What is (a_1)?HardLevel 54 If aₙ = 3 × 4ⁿ⁻¹, what is the value of a₄ + a₅?MediumLevel 54 In the geometric progression (11,22,44,\ldots), if (a_n=1408), what is (n)?HardLevel 54 If p, q, r and s are all non-zero terms, which of the following conditions proves that p, q, r, s, in this order, are terms of a geometric progression?HardLevel 54 What is the sum of the first (12) terms of the geometric progression (9,18,36,\ldots)?HardLevel 54 If (a_6=224) and (a=7), and (r) is positive, what is (r)?HardLevel 54 In the geometric progression (45,15,5,\frac{5}{3},\ldots), which term is (\frac{5}{27})?HardLevel 54 If (a=2) and (r=4), what is the value of (a_5+a_6)?HardLevel 54 How many terms of the geometric progression (2,6,18,\ldots) have sum (242)?HardLevel 54 In a geometric progression, (a_4=54) and (a_7=1458). What will be the positive common ratio (r)?ExpertLevel 53 Which of the following sequences is obtained by multiplying each term by the same non-zero constant to get the next term?ExpertLevel 53 What is the sixth term of the geometric progression (5,-15,45,-135,\ldots)?ExpertLevel 53 If (4,x,100) are consecutive terms of a positive geometric progression, what is the value of (x)?ExpertLevel 53 If (a_1=3) and (a_5=243), what will be the positive common ratio?ExpertLevel 53 In a geometric progression, (a_3=24) and (a_6=648). What is the value of (a_4)?ExpertLevel 53 Which sequence has both (a_2=18) and (a_5=486)?ExpertLevel 53 If \(a_n=2\cdot3^{n-1}\), what will be the value of \(a_4+a_6\)?ExpertLevel 53 In the geometric progression (160,80,40,20,\ldots), which term is (\frac{5}{2})?ExpertLevel 53 If a geometric progression has first term \(a=32\) and common ratio \(r=\frac12\), what is the sum of the first four terms?MediumLevel 53 If (x-2,x+4,2x+8) are consecutive positive terms of a geometric progression, what is (x)?ExpertLevel 53