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 geometric progression has (a=5) and (r=3) what is the value of (a_8)?HardLevel 54What is the ninth term of the geometric progression (256,128,64,32,\ldots)?HardLevel 54If (a_n=4\cdot3^{n-1}) which term will be (2916)?HardLevel 54In a geometric progression the first term is (6) and the fifth term is (486). If (r) is positive what is (r)?HardLevel 54What is the general term of the geometric progression (10,30,90,270,\ldots)?HardLevel 54What is the sum of the first (6) terms of the geometric progression (2,6,18,54,\ldots)?HardLevel 54If (8,x,72) are in geometric progression and (x>0), what is (x)?HardLevel 54If the common ratio of a geometric progression is negative, which statement about the signs of its consecutive terms is correct?HardLevel 54Let \(x, y, z\) be three consecutive non-zero terms of a geometric progression. Which of the following relation is always true?HardLevel 54What is the general term of the geometric progression (81,27,9,3,\ldots)?HardLevel 54For a geometric progression with (a=4) and (a_6=972), if (r) is positive what is (r)?HardLevel 54In the geometric progression (3, 12, 48, 192, …), which term is 3072?MediumLevel 54If \(a=96\) and \(r=\frac{1}{2}\), what is the value of \(a_7\)?HardLevel 54If the sum of the first 5 terms of a geometric progression is 242, with a = 2 and r = 3, which statement is correct?MediumLevel 54What is the sum of the first 7 terms of the geometric progression (1, 3, 9, 27, …)?MediumLevel 54In a geometric progression (a_3=20) and (a_6=160). If (r) is positive what is (r)?HardLevel 54Three non-zero numbers \(p, q, r\), in this order, form a geometric progression if which condition is true?HardLevel 54What is (a_8\div a_5) for the geometric progression (5,15,45,135,\ldots)?HardLevel 54If (a_n=7\cdot2^{n-1}), what is the sum of the first (6) terms?HardLevel 54Which term of the geometric progression (2,10,50,\ldots) is (1250)?HardLevel 54