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 …

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 \(\sqrt{2026{\mathrm{S}}_{2025}},\) then the absolute difference between \({20}^{\text{th }}\text{ and }{15}^{\text{th }}\) terms of the A.P. is