All of the positive integers are written in a triangular pattern, beginning with the following
four lines and continuing in the same way:
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
Which number appears directly below 2012?
Choose the correct choice:
A) 2100 B) 2102 C) 2104 D) 2106 E) 2108
Observe that the nth row has 2n- 1 numbers, that each number on the 2nth row is   equal to 2n-2 plus the one above it, and that the last number in the nth row is n2. (The latter   fact may be proved by observing that n2- (n- 1)2 = 2n- 1, the length of the nth row.)   442 = 1936 and 452 = 2025, so that 2012 is on the 45th row. The number below it will be   larger by (2 * 46- 2), so it will be 2102.   correct answer 2102
<result>B</result>
All of the positive integers are written in a triangular pattern, beginning with the following
four lines and continuing in the same way:
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
Which number appears directly below 2012?