Let S n = 1/2 + 1/6 + 1/12 + 1/20 + up to n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is √(2026 S₂₀₂₅), then the absolute difference between 20^(th) and 15^(th) terms of the A.P. is

Sequence and Series: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q62

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumSequence and Series179× since 2002

Let

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

up to

n

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

-p

and common difference

p

\sqrt{2026 S_{2025}}

, then the absolute difference between

20^{\text{th}}

and

15^{\text{th}}

terms of the A.P. is