The two triangular numbers that add up to 100 are 36 and 64. The triangular number sequence is generated by the formula ( T_n = \frac{n(n+1)}{2} ). For ( n = 8 ), ( T_8 = 36 ), and for ( n = 11 ), ( T_{11} = 64 ). Together, they satisfy the equation ( 36 + 64 = 100 ).
Square numbers.
When you add two consecutive triangular numbers, the result is a perfect square. For example, the first two triangular numbers are 1 (T1) and 3 (T2), and their sum is 4, which is (2^2). In general, the sum of the (n)-th triangular number (T_n) and the ((n+1))-th triangular number (T_{n+1}) equals ((n+1)^2). This relationship holds for all pairs of consecutive triangular numbers.
36 and 64
An example of two numbers which add together to make 100 are 47 and 53.
The two square numbers that add together to make 100 are 36 and 64. Specifically, (6^2 = 36) and (8^2 = 64). When you add them together, (36 + 64 = 100).
Square numbers.
When you add two consecutive triangular numbers, the result is a perfect square. For example, the first two triangular numbers are 1 (T1) and 3 (T2), and their sum is 4, which is (2^2). In general, the sum of the (n)-th triangular number (T_n) and the ((n+1))-th triangular number (T_{n+1}) equals ((n+1)^2). This relationship holds for all pairs of consecutive triangular numbers.
The square of the second number.
28 and 10 are both triangular numbers and add up to 38
36 and 64
An example of two numbers which add together to make 100 are 47 and 53.
62.5 and 37.5
121
50
The two square numbers that add together to make 100 are 36 and 64. Specifically, (6^2 = 36) and (8^2 = 64). When you add them together, (36 + 64 = 100).
6 and 10 are triangular numbers that make 16.
the answer is of course 12