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Triangular Numbers

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

MathematicsIf \(S_n=1+2+3+\cdots+n\), which of the following expressions is an odd perfect square for every natural number \(n\)?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_n=13041), what is the value of (n)?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_n=1830), what will be the value of (S_{3n})?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_{2n}=4095), what is the value of (n)?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_n=12246), what is the value of (n)?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_n=5050), what is the value of (S_{n+4}-S_n)?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_n=5995), what will be the value of (S_{n-8})?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_a=3003) and (S_b=5050), what will be the value of (b-a)?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf (S_n=2080), what will be the value of (S_{n+9})?Class 9Sequences and ProgressionsSum of first n natural numbersExpert MathematicsIf Sₙ − Sₙ₋₁ = 126 and Sₘ = 1953, what is n − m, where Sₖ = 1 + 2 + ⋯ + k?Class 9Sequences and ProgressionsSum of first n natural numbersMedium MathematicsIf \(S_n\) is the sum of the first \(n\) natural numbers, which of the following statements is always true for every positive integer \(n\)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf \(S_u=1431\) and \(S_v=3321\), what is the value of \(u+v\), where \(S_k=1+2+\cdots+k\)?Class 9Sequences and ProgressionsSum of first n natural numbersMedium MathematicsIf (S_{5p}=5050), what is the value of (p)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf (S_a=2485) and (S_b=3570), what will be the value of (b-a)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsWhich of the following sets represents numbers obtained as the sum of the first n natural numbers (triangular numbers)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf (S_{3k}=1176), what will be the value of (k)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf (S_n=465), what will be the value of (S_{n+5})?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf \(S_n\) denotes the sum of the first \(n\) natural numbers, which of the following statements is always true for every natural number \(n\)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf (S_n=4560), what is the value of (S_{n+5}-S_n)?Class 9Sequences and ProgressionsSum of first n natural numbersHard MathematicsIf a positive integer \(S\) can be written as the sum of the first \(n\) natural numbers, which of the following quantities must be an odd perfect square?Class 9Sequences and ProgressionsSum of first n natural numbersHard