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

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.

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

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

Consider the arithmetic progression 3,7,11,…and let \(A_n\) denote the sum of the first n terms of this progression.Then the value of \(\frac{1}{25}∑^{25}_{n=1}A_n\) is

The average of a non-decreasing sequence of N numbers \(a_1,a_2,…,a_N\) is 300.If \(a_1\) is replaced by \(6a_1\), the new average becomes 400.Then,the number of possible values of \(a_1\) is

On day one,there are 100 particles in a laboratory experiment.On day n,where n≥2,one out of every n particles produces another particle.If the total number of particles in the laboratory experiment increases to 1000 on day m,then m equals

For any natural number n,suppose the sum of the first n terms of an arithmetic progression is \((n+2n^2)\). If the \(n^{th}\) term of the progression is divisible by 9,then the smallest possible value of n is

Consider a sequence of real numbers \(x_1,x_2,x_3,…\) such that \(x_{n+1}=x_n+n−1\) for all \(n≥1\). If \(x_1=−1\) then \(x_{100}\) is equal to

For a sequence of real numbers \(x_1, x_2, ..., x_n,\) if \(x_1 - x_2 + x_3 - ... + (-1)^{n + 1}x_n =n^2 + 2n\) for all natural numbers n, then the sum \(x_{49} + x_{50}\) equals