Let \( S_n = \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \ldots \) upto \( n \) terms. If the sum of the first six terms of an A.P. with first term \( -p \) and common difference \( p \) is \( \sqrt{2026\, S_{2025}} \), then the absolute difference between \( 20^{\text{th}} \) and \( 15^{\text{th}} \) terms of the A.P. is:
