Given Series

1. Given number series: 2, 9, 28, 65, 126, ?

Question

What is the next number in this sequence?

Answer

217.

Solution

1. Compare terms with standard cubes ($n^3$):
2. 1^3 + 1 = 1 + 1 = 2
3. 2^3 + 1 = 8 + 1 = 9
4. 3^3 + 1 = 27 + 1 = 28
5. 4^3 + 1 = 64 + 1 = 65
6. 5^3 + 1 = 125 + 1 = 126
7. Pattern rule: $n^3 + 1$ where $n = 1, 2, 3, 4, 5, 6...$
8. Next term = 6^3 + 1 = 216 + 1 = 217.