Integrated Progressions

Calculus Level 3

let \(a_{n} =\displaystyle \int_{0}^{\pi/4}\tan^{n}x \mathrm{d}x\). Then \(a_{2} + a_{4}, a_{3}+a_{5},a_{4}+a_{6}\) are in what kind of progression?

This question is part of the set For the JEE-nius;P
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