What type of number is the sum of two consecutive triangular numbers?

Historical Note. According to David M. Burton, in his Elementary Number Theory, revised ed. of 1980, this result has been attributed to Plutarch, circa 100 C.E.

Is 16 a triangular number?

List Of Triangular Numbers. 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, and so on.

How do you find consecutive triangular numbers?

The triangular numbers are obtained by continued summation of the natural numbers. So, to get the triangular numbers first we will take the natural number and add 2 to it. So, we get the next number as 3.

How do you add consecutive triangular numbers?

We will now show that a triangular number — the sum of consecutive numbers — is given by this algebraic formula: ½n(n + 1), where n is the last number in the sum. (For example, n = 4 in the last sum above.)

What is the sum of consecutive squares?

The sum of consecutive squares Since a square number is composed of triangular numbers, then a sum of squares will be a sum of triangles. Now — if there were an equal number of 1’s, 2’s, and 3’s, then the sum of those 3 squares would be a multiple of the 3rd triangle, 1 + 2 + 3.

Are all odd numbers written as the sum of two consecutive numbers?

Many people spotted the pattern that all odd numbers (except 1) could be written as the sum of two consecutive numbers. For example, Matilda and Tamaris wrote: If you add two consecutive numbers together, the sum is an odd number, e.g. 1+2=3 2+3=5 3+4=7 4+5=9 5+6=11 6+7=13 and so on…

What is the sum of the first 50 even numbers?

Find the sum of the first 50 even numbers. 50 × 51 = 2550. For the sum of consecutive odd numbers, see Appendix 2. Just as a triangular number is a number that can appear as a triangle, so a square number can take the form of a square. 25 is a square number. Now, how are square numbers related to triangular numbers?

Can an even number of consecutive numbers add to make?

But if you add two consecutive numbers, the answer is always an odd number. So a sum like this must have an odd number as a factor again – but doesn’t. This proves that an even number of consecutive numbers cannot add to make .