Given a triangular number,how to find the next triangular number?

Each triangular number is half the product of 2 consecutive integers. 21 is a triangular number. Double it, get 42, which is 6•7, so the next triangular number is half of 7•8 = 56/2 = 28. If the number you're working with is large, after you double it, take the square root, which will fall between the 2 consecutive integers.