Consider the following sequence: 0, 6, 24, 60, 120, 210 Which one of t

Now, find the differences between these first differences (second differences):
18 – 6 = 12
36 – 18 = 18
60 – 36 = 24
90 – 60 = 30

Now, find the differences between these second differences (third differences):
18 – 12 = 6
24 – 18 = 6
30 – 24 = 6

Since the third differences are constant (6), the sequence is based on a cubic polynomial. A common pattern for such sequences is $n^3 – c \cdot n$ or similar. Let’s try $n^3 – n$:
For n=1: $1^3 – 1 = 1 – 1 = 0$ (Matches the first term)
For n=2: $2^3 – 2 = 8 – 2 = 6$ (Matches the second term)
For n=3: $3^3 – 3 = 27 – 3 = 24$ (Matches the third term)
For n=4: $4^3 – 4 = 64 – 4 = 60$ (Matches the fourth term)
For n=5: $5^3 – 5 = 125 – 5 = 120$ (Matches the fifth term)
For n=6: $6^3 – 6 = 216 – 6 = 210$ (Matches the sixth term)

The pattern is $a_n = n^3 – n$ for n = 1, 2, 3, …
The next number in the sequence will be the 7th term, for n=7.
$a_7 = 7^3 – 7 = 343 – 7 = 336$.