# 60+ CAT Progressions Questions With Video Solutions and PDF

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. These questions are compiled from all the past year CAT question papers.

## CAT Progressions And Series Weigthage Over Past 5 Years

 Year Weightage 2023 7 2022 5 2021 5 2020 2 2019 6 2018 5

## What are Sequences, Series and Progressions?

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 Formulas PDF

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.  AM GM HM Inequality Formulae: 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 ≥ G.M ≥ H.M

2. 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 ‘k’ 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. Geometric Progression - 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 ‘r’ is the common ratio).

Sum of ‘n’ 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 ‘k’ is a constant then

1. ak, bk, ck,...will also be in G.P
2. a/k, b/k, c/k will also be in G.P

Sum of term of infinite series in G.P, $$S_{∞}$$=$$\frac {a}{1-r}$$ (-1 < r <1)

## CAT 2023 Progressions and Series questions

#### Question 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

#### Question 2

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

#### Question 3

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

#### Question 4

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

#### Question 5

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

#### Question 6

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then the lowest possible value of n is

#### Question 7

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

## CAT 2022 Progressions and Series questions

#### Question 1

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

#### Question 2

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

#### Question 3

On day one, there are 100 particles in a laboratory experiment. On day n, where $$n\ge2$$, one out of every n articles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals

#### Question 4

The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is

#### Question 5

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 $$\frac{1}{25} \sum_{n=1}^{25} A_{n}$$ is

## CAT 2021 Progressions and Series questions

#### Question 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

#### Question 2

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

#### Question 3

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

#### Question 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

#### Question 5

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the 15th group is equal to

## CAT 2020 Progressions and Series questions

#### Question 1

If $$x_1=-1$$ and $$x_m=x_{m+1}+(m+1)$$ for every positive integer m, then $$X_{100}$$ equals

#### Question 2

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

## CAT 2019 Progressions and Series questions

#### Question 1

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