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Sequence Properties

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsThe sum of the first n terms of a sequence is \(S_n\), with \(S_0=0\). Which of the following conditions is necessary and sufficient to prove that the sequence is an arithmetic progression?Class 10Arithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APMedium MathematicsIf the nth term of an arithmetic progression is \(a_n=4-7(n-1)\), which of the following statements is correct?Class 10Arithmetic Progressions (AP)Finding the $n$th term of an APExpert MathematicsThe nth term of an arithmetic progression is given by \(a_n=7-4n\). Which statement about this AP is correct?Class 10Arithmetic Progressions (AP)Finding the $n$th term of an APExpert MathematicsIf the \(p\)th term of an AP is \(a_p\) and its common difference is \(d\), which relation correctly gives the \(n\)th term?Class 10Arithmetic Progressions (AP)Finding the $n$th term of an APExpert MathematicsIn an AP, if \(a_p=a_q\) for two distinct positive integers p and q, what type of AP must it be?Class 10Arithmetic Progressions (AP)Finding the $n$th term of an APHard MathematicsThe terms of a sequence are denoted by \(a_n\). Which of the following conditions, if true for every \(n\), guarantees that the sequence is an arithmetic progression?Class 10Arithmetic Progressions (AP)Finding the $n$th term of an APHard