Well...the fifth row is 1 5 10 10 5 1...but to possibley solve a problem you need a formula for example (x+y)^2
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No, these are triangular numbers.
The formula for the nth term is t(n) = n(n+1)/2
They are called triangular numbers because if you make one mark on the first line, two marks on the second, three on the third, etc you will generate these numbers and with each line the marks form a triangular shape.
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t(4) = 10 t(5) = 15 10 + 15 = 25
No. In order to be the sides of a right triangle, the square of one of the numbers must be the sum of the squares of the other two numbers. (the square of 9) + (the square of 10) = 181 but (the square of 15) = 225 .
The number 10 comes between 6 and 15. The numbers 3, 6, 10, 15, 21, and 28 are called TRIANGLE NUMBERS because they can be represented by lines of dots that form an equilateral triangle. They represent the additive sum 1+2+...+n which is equal to n (n+1)/2.
15
(n^2+n)/2