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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_3=45) and (a_6=1215). What is (a_1)?HardLevel 55 If a_n = 2 × 5^(n−1), what is the value of a₄ + a₅?MediumLevel 55 In the geometric progression (12,24,48,\ldots), if (a_n=1536), what is (n)?HardLevel 55 If (a_1=6) and (a_4=750), and (r) is positive, what is (a_5)?HardLevel 55 What is the sum of the first (9) terms of the geometric progression (15,30,60,\ldots)?HardLevel 55 If (a_7=320) and (a=5), and (r) is positive, what is (r)?HardLevel 55 In the geometric progression (96,48,24,12,\ldots), which term is (\frac{3}{2})?HardLevel 55 If (a=3) and (r=5), what is the value of (a_5+a_6)?HardLevel 55 How many terms of the geometric progression (4,12,36,\ldots) have sum (484)?HardLevel 55 What is the thirteenth term of the geometric progression (5,15,45,135,\ldots)?HardLevel 56 If \(x, y, z\) are three consecutive terms of a geometric progression and \(y\ne0\), which of the following relations must be true?HardLevel 56 What is the eighth term of the geometric progression (729,243,81,27,\ldots)?HardLevel 56 If (a_n=8\cdot2^{n-1}), which term will be (4096)?HardLevel 56 In a geometric progression, the first term is (9) and the fifth term is (2304). If (r) is positive, what is (r)?HardLevel 56 What is the general term of the geometric progression (14,42,126,378,\ldots)?HardLevel 56 What is the sum of the first 6 terms of the geometric progression (4, 12, 36, 108, ...)?HardLevel 56 If (18,x,200) are in geometric progression and (x>0), what is (x)?HardLevel 56 What is the sum of the first (5) terms of the geometric progression (6,30,150,750,\ldots)?HardLevel 56 Which of the following sequences is a geometric progression with a negative common ratio?HardLevel 56 What is the general term of the geometric progression (216,72,24,8,\ldots)?HardLevel 56