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Sequence Properties

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

MathematicsIf all terms of a geometric progression are positive and its common ratio is less than 1, which statement about its terms is correct?Class 9Sequences and ProgressionsGeometric ProgressionExpertMathematicsFor three consecutive non-zero terms \(a, b, c\) of a geometric progression, which of the following relations is always true?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsWhich of the following conditions is sufficient to identify a sequence with non-zero terms as a geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsWhich 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 ProgressionHardMathematicsAll terms of a sequence are non-zero. Which of the following conditions is sufficient to identify the sequence as a geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsWhich condition is necessary and sufficient for a sequence with non-zero terms to be a geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsIf all terms of a sequence are non-zero, which of the following conditions is sufficient to identify the sequence as a geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionExpertMathematicsIf 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 ProgressionHardMathematicsIf three non-zero real numbers \(x, y, z\) are in geometric progression in this order, which of the following condition is necessary and sufficient?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsThree non-zero numbers \(p, q, r\), in this order, form a geometric progression if which condition is true?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsLet \(x, y, z\) be three consecutive non-zero terms of a geometric progression. Which of the following relation is always true?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsIf the common ratio of a geometric progression is negative, which statement about the signs of its consecutive terms is correct?Class 9Sequences and ProgressionsGeometric ProgressionHardMathematicsWhich property identifies a non-zero geometric progression?Class 9Sequences and ProgressionsGeometric ProgressionEasyMathematicsWhen will four numbers \(p,q,r,s\), written in order, be consecutive terms of an arithmetic progression?Class 9Sequences and ProgressionsArithmetic ProgressionHardMathematicsIf the terms at two distinct positions in an arithmetic progression are equal, which conclusion is necessary?Class 9Sequences and ProgressionsArithmetic ProgressionHardMathematicsA sequence is defined by the recursive rule \(a_{n+1}=a_n+2n\), where \(n\geq 1\). Which statement about this sequence must be true?Class 9Sequences and ProgressionsRecursive ruleHard

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