Determine whether or not 630 is a triangular number. start with the formula t n = n (n + 1) 2 and then use the quadratic formula to make your decision. (a) true or false: 630 is a triangular number:

Triangular sequence = n (n + 1) / 2

If 630 is a triangular number, then:

n (n + 1) / 2 = 630

Then n should be a positive whole number if 630 is a triangular number.

n (n + 1) / 2 = 630

n (n + 1) = 2*630

n (n + 1) = 1260

n² + n = 1260

n² + n - 1260 = 0

By trial an error note that 1260 = 35 * 36

n² + n - 1260 = 0

Replace n with 36n - 35n

n² + 36n - 35n - 1260 = 0

n (n + 36) - 35 (n + 36) = 0

(n + 36) (n - 35) = 0

n + 36 = 0 or n - 35 = 0

n = 0 - 36, or n = 0 + 35

n = - 36, or 35

n can not be negative.

n = 35 is valid.

Since n is a positive whole number, that means 630 is a triangular number.

So the answer is True.