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Algebraic Condition

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

MathematicsAll terms of a sequence are non-zero. Which of the following conditions, if true for every suitable n, confirms that the sequence is a geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionExpert MathematicsWhich condition is necessary and sufficient for three consecutive non-zero terms \(a,b,c\) of a sequence to be in geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionHard MathematicsIf three non-zero numbers \(x, y, z\), in this order, are consecutive terms of a geometric progression, which relation must hold?Class 9Sequences and ProgressionsGeometric ProgressionHard 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 ProgressionExpert 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 ProgressionHard MathematicsThree distinct numbers \(p, q, r\), in this order, are consecutive terms of an arithmetic progression. Which condition ensures this?Class 9Sequences and ProgressionsArithmetic ProgressionHard