Answer:
8
Step-by-step explanation:
first number = a, there are n numbers
so last number is a + n - 1
sum = [a + (a + n - 1)} * n/2 = (2a + n - 1) / 2 = 2012
n * (2a + n - 1) = 2012 * 2 = 4024
4024 is even, so n must be even, divisible by 2, 4, 8
4024 = 2 * 2012 = 4 * 1006 = 8 * 503
If n = 2, 2a + n - 1 = 2012, 2a + 2 - 1 = 2012, 2a = 2011, impossible.
If n = 4, 2a + n - 1 = 1006, 2a + 4 - 1 = 2a + 3 = 1006, 2a = 1003, impossible
If n = 8, 2a + n - 1 = 503, 2a + 8 - 1 = 2a + 7 = 503, a = 248
so n = 8, a = 248
