CAT Progressions and series questions come under arithmetics. These are the most commonly asked questions in the CAT exam. These questions are based on the mathematical concepts of sequences, series, and progressions. This is one of the important topics that aspirants should pay attention to. Make use of the below free questions for practising. Take free CAT mocks to understand the exam pattern and also you'll get a fair idea of how questions are asked. If you're weak in Progressions and Series questions for CAT, make sure you learn the basic concepts well. Here, you can learn all the important formulas from CAT Progressions and Series. You can check out these CAT Progression and Series Questions PDF from the CAT Previous year's papers. You can download them in a PDF format or take them in a test format. And the best part is you will find detailed video solutions for every question the CAT experts explain. Click on the below link to download the CAT progressions and series questions with detailed video solutions PDF.Â These questions are compiled from all theÂ past year CAT question papers.
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Year |
Weightage |
2023 | 7 |
2022 |
5 |
2021 |
5 |
2020 |
2 |
2019 |
6 |
2018 |
5 |
Sequences: A sequence is a set of numbers arranged in a particular order. A sequence can be finite or infinite. An example of a finite sequence is {2, 4, 6, 8}, and an example of an infinite sequence is {1, 2, 3, 4, ...}.
Series: A series is the sum of the terms of a sequence. For example, the sum of the first n natural numbers is given by the series 1 + 2 + 3 + ... + n.
Progressions: A progression is a sequence in which each term is obtained by adding a constant to the preceding term. There are different types of progressions, such as arithmetic progression, geometric progression, and harmonic progression.
CAT Progressions and series are one of the most important topics in the quantitative aptitude section, and it is vital to have a clear understanding of the formulas related to them. As mentioned earlier, the questions related to this topic were commonly asked in the CAT exam. To help the aspirants to ace this topic, we have made a PDF containing a comprehensive list of formulas, tips, and tricks that you can use to solve Progressions and series questions with ease and speed. Click on the below link to download the CAT Progressions and series formulas PDF.
1. Â AM GM HM InequalityÂ Formulae:Â Relationship between AM, GM and HM for two numbers a and b,
A.M=$$\frac{a+b}{2}$$
G.M=$$\sqrt{a \times b}$$
H.M=$$\frac{2ab}{a+b}$$
G.M=$$\sqrt{AM \times HM}$$
A.M â‰¥ G.M â‰¥ H.M
2.Â Arithmetic progression (A.P)
- Formulas and Properties
If the sum of the difference between any two consecutive terms is constant then the terms are said to be in A.P
Example: 2,5,8,11 or a, a+d, a+2d, a+3d...
If 'a' is the first term and 'd' is a common difference then the general 'n' term is $$T_{n}$$=a+(n-1)d
Sum of first 'n' terms in A.P=$$\frac{n}{2}$$[2a+(n-1)d]
Number of terms in A.P=$$\frac{Last Term-First Term}{Common Difference}$$+1
Properties of Arithmetic progression
If a, b, c, d,.... are in A.P and â€˜kâ€™ is a constant then
a-k, b-k, c-k,... will also be in A.P
ak, bk, ck,...will also be in A.P
a/k, b/k, c/k will also be in A.P
3.Â Geometric ProgressionÂ - Formulas and Properties
If in a succession of numbers the ratio of any term and the previous term is constant then that numbers are said to be in Geometric Progression.
Ex :1, 3, 9, 27 or a, ar, a$$r^{2}$$, a$$r^{3}$$
The general expression of a G.P, Tn = a $$r^{n-1}$$ (where a is the first term and â€˜râ€™ is the common ratio).
Sum of â€˜nâ€™ terms in G.P, Sn = $$\frac{a(1-r^{n})}{1-r}$$ (if r<1) or $$\frac {a(r^{n}-1)}{r-1}$$ (if r>1)
Properties of G.P
If a, b , c, d,.... are in G.P and â€˜kâ€™ is a constant then
Sum of term of infinite series in G.P, $$S_{âˆž}$$=$$\frac {a}{1-r}$$ (-1 < r <1)
For a real number x, if $$\frac{1}{2}, \frac{\log_3(2^x - 9)}{\log_3 4}$$, and $$\frac{\log_5\left(2^x + \frac{17}{2}\right)}{\log_5 4}$$ are in an arithmetic progression, then the common difference is
correct answer:-4
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
correct answer:-2
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
correct answer:-2
The value of $$1 + \left(1 + \frac{1}{3}\right)\frac{1}{4} + \left(1 + \frac{1}{3} + \frac{1}{9}\right)\frac{1}{16} + \left(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27}\right)\frac{1}{64} + -------$$ is
correct answer:-4
Let $$a_n = 46 + 8n$$ and $$b_n = 98 + 4n$$ be two sequences for natural numbers $$n \leq 100$$. Then, the sum of all terms common to both the sequences is
correct answer:-1
A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on theÂ first day, the number of organisms on any day is equal to 3 more than twice the number on the previousÂ day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is
correct answer:-19
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
correct answer:-967
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
correct answer:-14
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
correct answer:-3
On day one, there are 100 particles in a laboratory experiment. On day n, where $$n\ge2$$, one out of every n articlesÂ produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals
correct answer:-1
The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is
correct answer:-548
Consider the arithmetic progression 3, 7, 11, ... and let $$A_n$$ denote the sum of the first n terms of this progression.Â Then the value of $$\frac{1}{25} \sum_{n=1}^{25} A_{n}$$ is
correct answer:-1
Three positive integers x, y and z are in arithmetic progression. If $$y-x>2$$ and $$xyz=5(x+y+z)$$, then z-x equals
correct answer:-3
Consider a sequence of real numbers, $$x_{1},x_{2},x_{3},...$$ such that $$x_{n+1}=x_{n}+n-1$$ for all $$n\geq1$$. If $$x_{1}=-1$$ then $$x_{100}$$ is equal to
correct answer:-4
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
correct answer:-4
If $$x_0 = 1, x_1 = 2$$, and $$x_{n + 2} = \frac{1 + x_{n + 1}}{x_n}, n = 0, 1, 2, 3, ......,$$ then $$x_{2021}$$ is equal to
correct answer:-4
The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), â€¦.. and so on. Then, the sum of the numbers in the 15th group is equal to
correct answer:-1
If $$x_1=-1$$ and $$x_m=x_{m+1}+(m+1)$$ for every positive integer m, then $$X_{100}$$ equals
correct answer:-1
Let the m-th and n-th terms of a geometric progression be $$\frac{3}{4}$$ and 12. respectively, where $$m < n$$. If the common ratio of the progression is an integer r, then the smallest possible value of $$r + n - m$$ is
correct answer:-4
If $$a_1, a_2, ......$$ are in A.P., then, $$\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + ....... + \frac{1}{\sqrt{a_n} + \sqrt{a_{n + 1}}}$$ is equal to
correct answer:-1