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_3=18) and (a_7=1458), what is the positive value of (r)?HardLevel 55In the geometric progression (1024,512,256,128,\ldots), which term is (2)?HardLevel 55If (a=11) and (a_6=352), and (r) is positive, what is (r)?HardLevel 55What is the sum of the first (6) terms of the geometric progression (9,27,81,\ldots)?HardLevel 55In a geometric progression (a_2=16) and (a_5=1024). If (r) is positive, what is (a_1)?HardLevel 55If the sixth term of the geometric progression (x,,3x,,9x,\ldots) is (2430), what is (x)?HardLevel 55How many terms are there up to (2048) in the geometric progression (2,8,32,\ldots)?HardLevel 55If the first (4) terms of a geometric progression are (3,15,75,375), what is (S_4)?HardLevel 55Which term of the geometric progression (10,40,160,\ldots) is (10240)?HardLevel 55If (a_1=4) and (r=-3), what is (a_5)?HardLevel 55What is the sum of the first (4) terms of the geometric progression (2,14,98,686,\ldots)?HardLevel 55If (a_3=72) and (r=2), what is the value of (a_9)?HardLevel 55In the geometric progression (405,135,45,\ldots), which term is (5)?HardLevel 55If (a=8), (r=3), and (S_4=320), what is the statement?HardLevel 55What is the value of a₆ + a₇ for the geometric progression (2,6,18,...)?MediumLevel 55If \(a_n=128\left(\frac{1}{2}\right)^{n-1}\), which term will be equal to (8)?HardLevel 55What is the sum of the first (10) terms of the geometric progression (5,10,20,\ldots)?HardLevel 55All terms of a sequence are non-zero. Which of the following conditions is sufficient to identify the sequence as a geometric progression?HardLevel 55Which condition is necessary and sufficient for three consecutive non-zero terms \(a,b,c\) of a sequence to be in geometric progression?HardLevel 55If (a=162) and (r=\frac{1}{3}), what is the sum of the first (5) terms?HardLevel 55