Quote:
the nth term in sequence Q equals the absolute value of the difference between the nth smallest positive perfect cube and the (n-1)st smallest positive perfect cube.
Translate this. Q = 1, |8-1|, |27-8|, ... so on.
Observe two things here. First, the absolute value sign makes no difference because the difference will always be positive.
So you may even imagine it as
Q = 1, 8-1, 27-8, ... so on.
Second, when you sum all the values, pairs such as 1 and -1, and 8 and -8 get cancelled out, leaving
only the nth smallest positive perfect cube of the last (or the nth) term in the sum.Quote:
The sum of the first seven terms in sequence Q is
Now you can imagine that this will only leave out \(7^3\) as it is the last term in the sum.
Hence, D is the correct answer.