List of top Mathematics Questions on Sequence and series asked in WBJEE

Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If \(a_n\) and \(b_n\) be the \(n\)-th term of A.P. and G.P. respectively, then:
If for the series \(a_1, a_2, a_3, \ldots\), etc., \(a_{n+1} - a_n\) bears a constant ratio with \(a_n + a_{n+1}\), then \(a_1, a_2, a_3, \ldots\) are in:
If \( a_1, a_2, \dots, a_n \) are in A.P. with common difference \( \theta \), then the sum of the series:
\[ \sec a_1 \sec a_2 + \sec a_2 \sec a_3 + \dots + \sec a_{n-1} \sec a_n = k (\tan a_n - \tan a_1), \]
where \( k = ? \)