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Common Ratio

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf (6,18,54,\ldots) is a geometric progression, what is the value of (a_5-a_3)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsIf three non-zero numbers \(a, b, c\), in this order, are consecutive terms of a geometric progression, which of the following condition is necessary and sufficient?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsIf \(a_1=\frac{3}{2}\) and \(r=4\), what will be \(a_5\)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsWhich sequence has a₃ = 50 and common ratio r = 5?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Easy MathematicsIf \(a_n=48\left(\frac{1}{2}\right)^{n-1}\), what is the value of \(a_3+a_5\)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsIn the geometric progression (a, ar, ar², …), if a₂ + a₃ = 30 and r = 2, what is a₁?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Medium MathematicsIf a₂ = 10 and a₆ = 160 in a geometric progression, and the common ratio is positive, what is a₁?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Medium MathematicsIf (a_1=3) and (a_5=243), what will be the positive common ratio?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsWhich of the following sequences is obtained by multiplying each term by the same non-zero constant to get the next term?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsIn a geometric progression, (a_4=54) and (a_7=1458). What will be the positive common ratio (r)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 53Expert MathematicsIf (a_6=224) and (a=7), and (r) is positive, what is (r)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsIf p, q, r and s are all non-zero terms, which of the following conditions proves that p, q, r, s, in this order, are terms of a geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsAll 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?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsA 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?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsIf (a=3) and (a_7=192), and (r) is positive, what is (r)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsFor a geometric progression with (a=4) and (a_6=972), if (r) is positive what is (r)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsIf the common ratio of a geometric progression is negative, which statement about the signs of its consecutive terms is correct?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsIn a geometric progression the first term is (6) and the fifth term is (486). If (r) is positive what is (r)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsIf a geometric progression has (a=5) and (r=3) what is the value of (a_8)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 54Hard MathematicsIf (a_n=768) in (3,12,48,192,\ldots), what is (n)?Class 9Sequences and ProgressionsGeometric ProgressionLevel 55Medium