What should be the next number in the sequence given below ? 2, 8, 18, 32, 50, _ ?

The given sequence follows a clear mathematical pattern that can be solved using two methods:

• Method 1 (n-th term formula): The sequence follows the formula 2n², where 'n' represents the position of the term. For n=1, 2(1)²=2; for n=2, 2(2)²=8; for n=3, 2(3)²=18; for n=4, 2(4)²=32; and for n=5, 2(5)²=50. Therefore, for the 6th term (n=6), the value is 2(6)² = 2 × 36 = 72.
• Method 2 (Difference of differences): The differences between consecutive terms are 6, 10, 14, and 18. These differences increase by a constant value of 4. The next difference should be 18 + 4 = 22. Adding this to the last term: 50 + 22 = 72.

Notably, this sequence also corresponds to the maximum number of electrons in atomic shells (K, L, M, N, O, P) based on the Bohr-Bury rule.