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_2=12) and (a_5=324), what is the positive value of (r)?HardLevel 54In the geometric progression (729,243,81,27,\ldots), which term is (1)?HardLevel 54If (a=3) and (a_7=192), and (r) is positive, what is (r)?HardLevel 54What is the sum of the first (7) terms of the geometric progression (4,12,36,\ldots)?HardLevel 54In a geometric progression (a_3=48) and (a_6=384). If (r) is positive what is (a_1)?HardLevel 54If the fifth term of the geometric progression (x,,2x,,4x,\ldots) is (80), what is (x)?HardLevel 54How many terms are there up to 1024 in the geometric progression (1, 4, 16, …)?MediumLevel 54If the first (4) terms of a geometric progression are (2,8,32,128), what is (S_4)?HardLevel 54Which term of the geometric progression (6,24,96,\ldots) is (6144)?HardLevel 54A plant produces 160 units on the first day, and on each following day its production becomes \(\frac{3}{2}\) times that of the previous day. A student states that the total production for the first four days is 1120 because 160 units were added each day. Which conclusion is correct?HardLevel 54What is the sum of the first (5) terms of the geometric progression (3,15,75,375,\ldots)?HardLevel 54If (a_4=80) and (r=2), what is the value of (a_9)?HardLevel 54In the geometric progression (512,256,128,\ldots), which term is (4)?HardLevel 54If (a=6), (S_4=240), and (r=3), what is the statement?HardLevel 54What is the value of a₅ + a₆ for the geometric progression (8, 24, 72, …)?HardLevel 54If \(a_n=100\left(\frac{1}{2}\right)^{n-1}\), which term will be equal to \(\frac{25}{2}\)?HardLevel 54What is the sum of the first (10) terms of the geometric progression (4,8,16,\ldots)?HardLevel 54If three non-zero real numbers \(x, y, z\) are in geometric progression in this order, which of the following condition is necessary and sufficient?HardLevel 54All terms of a sequence are non-zero, and for every interior term, \(a_n^2=a_{n-1}a_{n+1}\). Which conclusion about the sequence is definitely true?HardLevel 54If a = 81 and r = 1/3, what is the sum of the first 5 terms of the geometric progression?MediumLevel 54