List of top Quantitative Ability and Data Interpretation Questions on Sequences and Series

Given that \( 1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \dots = \frac{\pi^2}{6} \), the value of \( 1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \dots \) is
The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the 4th term of the progression is
Let \( S_1 = \{100, 105, 110, 115, \dots\} \) and \( S_2 = \{100, 95, 90, 85, \dots \} \) be two series in arithmetic progression. If \(a_k\) and \(b_k\) are the k-th terms of \(S_1\) and \(S_2\), respectively, then \( \sum_{k=1}^{20} a_k b_k \) equals ________