List of top Quantitative Aptitude Questions on Progressions (AP & GP)

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is

For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is:

In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?
Let $a_n$ be the $n^{\text{th}}$ term of a decreasing infinite geometric progression. If $a_1 + a_2 + a_3 = 52$ and $a_1a_2 + a_2a_3 + a_3a_1 = 624$, then the sum of this geometric progression is:
In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?
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
Suppose $x_1, x_2, x_3, \dots, x_{100}$ are in arithmetic progression such that $x_5 = -4$ and $2x_6 + 2x_9 = x_{11} + x_{13}$. Then, $x_{100}$ equals ?
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
The terms \(x_5 = -4\), \(x_1, x_2, \dots, x_{100}\) are in an arithmetic progression (AP). It is also given that \(2x_6 + 2x_9 = x_{11} + x_{13}\). Find \(x_{100}\).
Let both the series \(a_1,a_2,a_3,....\) and \(b_1,b_2,b_3,....\) be in arithmetic progression such that the common differences of both the series are prime numbers. If \(a_5=b_9,a_{19}=b_{19}\) and \(b_2=0\) , then \(a_{11}\) equals
For some positive and distinct real numbers \(x ,y\), and \(z\) , if \(\frac{1}{\sqrt{ y}+ \sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+ \sqrt{z}}\) and \(\frac{1}{\sqrt{x} +\sqrt{y}}\) , then the relationship which will always hold true, is
The value of \(1+\bigg(1+\frac{1}{3}\bigg)\frac{1}{4}+\bigg(1+\frac{1}{3}+\frac{1}{9}\bigg)\frac{1}{16}+\bigg(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\bigg)\frac{1}{64}+....\),is
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
The average of all 3-digit terms in the arithmetic progression 38,55,72,...,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
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
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