What's the math. algorith for 1,2,4,9,16,25,36,49,...etc.?

Answer 1

n^2 (n squared)
it's usually understood that n is a positive integer n=1,2,3,4...

Answer 2

Opposite Change Rule
The Opposite Change rule is not a standard algorithm; it is only a tool to help simplify addition of a pair of numbers. The rule says that the sum of two numbers is not changed if one subtracts a number from one addend and adds the same number to the other addend. This can be used to make an addition problem easier by making one of the two addends end in one or more zeroes. The process is not uniquely specified, obviously. In the problem at right, 185 + 266, we might have used the rule to change the expression into 190 + 261, or into 181 + 270, but then the resulting addition problem still requires carrying. In that case I suppose that we can iterate, continuing to simplify the same term, but the Everyday Mathematics student text assumes that a single application of the rule will turn the problem into one that the pupil can do without further difficulty.
185 -> 200
+ 266 + 251
--- ---
451


A nastier case for the Opposite Change rule would be 185 + 263. If we apply the rule to change the first term into 180 or 190, or to change the second term into 260 or 270, then the resulting problem still involves carrying (besides which, we may have to do a subtraction with borrowing in making the change to the other term). We can change the 185 to 200 but then have to do a subtraction with borrowing on the other term. The cleanest application in this case may be the one shown at right, but this just goes to illustrate that the Opposite Change rule is truly not a standard algorithm.
??
185 -> 205
+ 263 + 243
--- ---
448

Answer 3

nearest perfect square number
1, 2, 4, 9, 16, 25, 36, 49 etc

Answer 4

n^2 isn't right because what would equal 2???

Answer 5

y=x squared