Mathematics

Problem

Let

S_n = \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \dots

upto

n

terms. If the sum of the first six terms of an A.P. with first term

-p

and common difference

p

\sqrt{2026S_{2025}}

, then the absolute difference between 20th and 15th terms of the A.P. is (a) 25 (b) 90 (c) 20 (d) 45