The ancient greeks were very interested in number patterns.

C) a(n) = ⁿ⁽ⁿ ⁺ ¹⁾/₂

Step-by-step explanation:

We can plug in, for example, 1 for n. And if n = 1, since it is the first number of the sequence, the new number should also be 1.

A) 2 * n --> 2 * 1 --> 2; 2 ≠ 1, so A is incorrect.

B) n²/2 --> 1²/2 --> 1/2; 1/2 ≠ 1, so B is also incorrect.

C) 1(1 + 1)/2 --> 2/2 --> 1; 1 = 1, so C could be correct.

D) (1  + 1)/2 --> 2/2 --> 1; 1 = 1, so D could be correct.

Since either C or D could be correct, we can plug in n = 2 to see if it will be 3.

C) 2(2 + 1)/2 --> 6/2 --> 3; 3 = 3, so C could be correct.

D) (2 + 1)/2 --> 3/2 --> 3/2 ≠ 3, so D is not correct.

From this, we can conclude that C is the correct answer.

answer: -8.2562234e+13