List of top Quantitative Aptitude Questions on Sequence and Series asked in CAT

Consider the sequence\( t_1 = 1, t_2 = -1 and  t_n = \left( \frac{n-3}{n-1} \right) t_{n-2} for n \ge 3. \)Then, the value of the sum  \(\frac{1}{t_2}\) + \(\frac{1}{t_4}\) + \(\frac{1}{t_6}\) + ……. + \(\frac{1}{t_{2022}}\) + \(\frac{1}{t_{2024}}\), is

The sum of the infinite series \( \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \frac{1}{5} - \frac{1}{7} \right)^2 - \left( \frac{1}{7} \right)^2 + \left( \frac{1}{5} \right)^3 \left( \frac{1}{5} - \frac{1}{7} \right)^3 + \dots \) is equal to

A shopkeeper sells half of the grains plus \(3 \, \text{kg}\) of grains to Customer 1, and then sells another half of the remaining grains plus \(3 \, \text{kg}\) to Customer 2. When the 3rd customer arrives, there are no grains left. Find the total grains that were initially present.

Let \(a_n\) and \(b_n\) be two sequences such that \(a_n=13+6(n-1)\) and \(b_n=15+7(n-1)\) for all natural numbers \(n\) . Then, the largest three digit integer that is common to both these sequences, is