Without drawing a diagram, find 10th square number       (ii)  6th triangular number

The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the n^(th) triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . The number of positive integers lying between t_(100) and t_(101) are

The sum of two consecutive triangular numbers is a square number.

If 70% of 5//7^(th) of a number is 90 , find the number .

The unit digit of a two-digit number is 6. If 9 is added to the number, then the number obtained is 5//4th of the number itself. Find the sum of the digits

Find the 960^(th) and 961^(th) terms of the sequence given by: t_(n)={(n/(n/96-1), "if n is not the square of a natural number"),(6 1/2, "if n is the square of a natural number"):}

The average of twelve numbers is 58. The average of the first five numbers is 56 and the average of the next four numbers is 60. The 10^(th) number is one more than the 11^(th) number and the 11^(th) number is one less than the 12^(th) number. What is the average of the 10^(th) and 12^(th) numbers

The average of ten numbers is 72. The average of the first four numbers is 69 and that of the next three numbers is 74. The 8^(th) number is 6 more than the 9^(th) number and 12 more than the 10^(th) number. What is the average of the 8^(th) and 9^(th) numbers?