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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

For a geometric progression with (a=2) and (a_7=1458), if (r) is positive, what is (r)?HardLevel 56 In the geometric progression (8,32,128,512,\ldots), which term is (8192)?HardLevel 56 If \(a=256\) and \(r=\frac{1}{2}\), what is the value of \(a_9\)?HardLevel 56 If the sum of the first 4 terms of a geometric progression is stated to be 780 with a = 12 and r = 4, what is the correct evaluation?HardLevel 56 What is the sum of the first 6 terms of the geometric progression (5, 20, 80, 320, ...)?HardLevel 56 In a geometric progression (a_3=36) and (a_7=576). If (r) is positive, what is (r)?HardLevel 56 Which of the following conditions is sufficient to identify a sequence with non-zero terms as a geometric progression?HardLevel 56 What is (a_9\div a_5) for the geometric progression (9,27,81,243,\ldots)?HardLevel 56 If (a_n=6\cdot4^{n-1}), what is the sum of the first (5) terms?HardLevel 56 Which term of the geometric progression (7,21,63,\ldots) is (5103)?HardLevel 56 If (a_2=20) and (a_6=5120), what is the positive value of (r)?HardLevel 56 In the geometric progression (640,320,160,80,\ldots), which term is (5)?HardLevel 56 If (a=13) and (a_6=416), and (r) is positive, what is (r)?HardLevel 56 What is the sum of the first (6) terms of the geometric progression (11,33,99,\ldots)?HardLevel 56 In a geometric progression (a_3=80) and (a_6=5120). If (r) is positive, what is (a_1)?HardLevel 56 If the fifth term of the geometric progression (x,,4x,,16x,\ldots) is (1280), what is (x)?HardLevel 56 How many terms are there up to (12288) in the geometric progression (3,12,48,\ldots)?HardLevel 56 If the first (4) terms of a geometric progression are (5,25,125,625), what is (S_4)?HardLevel 56 Which term of the geometric progression (9,36,144,\ldots) is (9216)?HardLevel 56 If (a_1=6) and (r=-2), what is (a_7)?HardLevel 56