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.
Answer:
c 44
Step-by-step explanation:
2 digit meaning that it has 2 numbers. For example, 66 is a two digit number.
Now, they also said it must be prime, meaning that its factors can only be 1 and itself.
Also, it must be odd.
Answer: 67
Now, do the same, except the number must be composite, as meaning that it has other factors.
Answer: 21
I believe the correct answer from the choices listed above is the second option. If an oxygen atom has 8 protons and 10 neutrons in its nucleus, then its atomic number would be 8. The atomic number is <span>the number of protons in the nucleus of an atom. Hope this answers the question.</span>
