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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 numbersLevel 61Expert MathematicsIf (S_n=13041), what is the value of (n)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 61Expert MathematicsIf (S_n=1830), what will be the value of (S_{3n})?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 61Expert MathematicsIf (S_{2n}=4095), what is the value of (n)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 61Expert MathematicsIf (S_n=12246), what is the value of (n)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 60Expert MathematicsIf (S_n=5050), what is the value of (S_{n+4}-S_n)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 60Expert MathematicsIf (S_n=5995), what will be the value of (S_{n-8})?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 59Expert MathematicsIf (S_a=3003) and (S_b=5050), what will be the value of (b-a)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 59Expert MathematicsIf (S_n=2080), what will be the value of (S_{n+9})?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 59Expert MathematicsIf \(S_n-S_{n-1}=126\) and \(S_m=1953\), what is \(n-m\), where \(S_k=1+2+\cdots+k\)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 62Medium 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 numbersLevel 62Hard 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 numbersLevel 62Medium MathematicsIf (S_{5p}=5050), what is the value of (p)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 62Hard MathematicsIf (S_a=2485) and (S_b=3570), what will be the value of (b-a)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 62Hard 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 numbersLevel 61Hard MathematicsIf (S_{3k}=1176), what will be the value of (k)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 61Hard MathematicsIf (S_n=465), what will be the value of (S_{n+5})?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 61Hard 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 numbersLevel 60Hard MathematicsIf (S_n=4560), what is the value of (S_{n+5}-S_n)?Class 9Sequences and ProgressionsSum of first n natural numbersLevel 60Hard 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 numbersLevel 60Hard