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
What is the sum of the first (4) terms of the geometric progression (3,18,108,648,\ldots)?HardLevel 56If (a_4=96) and (r=2), what is the value of (a_{10})?HardLevel 56In the geometric progression (810,270,90,\ldots), which term is (10)?HardLevel 56If (a=10), (r=3), and (S_5=1210), what is the statement?HardLevel 56What is the value of a₅ + a₆ for the geometric progression (4, 16, 64, ...)?HardLevel 56If \(a_n=162\left(\frac{1}{3}\right)^{n-1}\), which term will be equal to (2)?HardLevel 56What is the sum of the first (9) terms of the geometric progression (7,14,28,\ldots)?HardLevel 56For three consecutive non-zero terms \(a, b, c\) of a geometric progression, which of the following relations is always true?HardLevel 56If three non-zero numbers \(a, b, c\) are consecutive terms of a geometric progression in this order, which relation must be true?HardLevel 56If (a=128) and (r=\frac{1}{2}), what is the sum of the first (5) terms?HardLevel 56In a geometric progression, (a_2=24) and (a_5=648). What is (a_1)?HardLevel 56If aₙ = 4 × 5ⁿ⁻¹, what is the value of a₄ + a₅?HardLevel 56In the geometric progression (18,36,72,\ldots), if (a_n=2304), what is (n)?HardLevel 56If (a_1=8) and (a_4=216), and (r) is positive, what is (a_5)?HardLevel 56What is the sum of the first (8) terms of the geometric progression (20,40,80,\ldots)?HardLevel 56If (a_8=1792) and (a=7), and (r) is positive, what is (r)?HardLevel 56In the geometric progression (150,50,\frac{50}{3},\frac{50}{9},\ldots), which term is (\frac{50}{81})?HardLevel 56If (a=5) and (r=4), what is the value of (a_5+a_6)?HardLevel 56How many terms of the geometric progression (6,18,54,\ldots) have sum (2184)?HardLevel 56Which of the following sequences is a geometric progression in which each term is obtained by multiplying the preceding term by the same fixed number?ExpertLevel 54