Is 297 a triangular number

Answer 1

The formula for finding the nth triangular number is: tn = n(n+1)/2.

If 297 is the nth triangular number then 297 = n(n+1)/2

Now we have a equation, if the solution of the equation is a natural number then 297 is a triangular number otherwise it is not.

297 = n(n+1)/2

297 x 2 = n2 + n

n2 + n = 594

n2 + n - 594 = 0, which is a quadratic equation.

And the solutions of the equation are:

n = (-1 - (2377)1/2)/2

n = ((2377)1/2 - 1)/2

As it can be seen the value of n is not a natural number so 297 can't be triangular number.

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