# Top 55 CAT Progressions and Series Questions With Solutions

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. These questions are compiled from past CAT question 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.

## CAT Progressions And Series Weigthage Over Past 5 Years

 Year Weightage 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.

## 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

#### Question 2

Let $$a_1, a_2, ...$$ be integers such that
$$a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$$ for all $$n \geq 1.$$
Then $$a_{51} + a_{52} + .... + a_{1023}$$ equals

#### Question 3

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

#### Question 4

If $$a_1 + a_2 + a_3 + .... + a_n = 3(2^{n + 1} - 2)$$, for every $$n \geq 1$$, then $$a_{11}$$ equals

#### Question 5

If $$(2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280$$, then whatis the value of $$1 + 2 + 3 + .. + n?$$

#### Question 6

The number of common terms in the two sequences: 15, 19, 23, 27, . . . . , 415 and 14, 19, 24, 29, . . . , 464 is

## CAT 2018 Progressions and Series questions

#### Question 1

Let $$t_{1},t_{2}$$,... be real numbers such that $$t_{1}+t_{2}+…+t_{n} = 2n^{2}+9n+13$$, for every positive integer $$n \geq 2$$. If $$t_{k}=103$$, then k equals

#### Question 2

Let $$\ a_{1},a_{2}...a_{52}\$$ be positive integers such that $$\ a_{1}$$ < $$a_{2}$$ < ... < $$a_{52}\$$. Suppose, their arithmetic mean is one less than arithmetic mean of $$a_{2}$$, $$a_{3}$$, ....$$a_{52}$$. If $$a_{52}$$= 100, then the largest possible value of $$a_{1}$$is

#### Question 3

The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

#### Question 4

The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u=(x+y)/2 and v=(y+z)/2. If x ≥ z, then the minimum possible value of x is

#### Question 5

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

## CAT 2017 Progressions and Series questions

#### Question 1

If $$a_{1}=\frac{1}{2\times5},a_{2}=\frac{1}{5\times8},a_{3}=\frac{1}{8\times11},...,$$ then $$a_{1}+a_{2}+a_{3}+...+a_{100}$$ is

#### Question 2

Let $$a_1$$, $$a_2$$,.............,  $$a_{3n}$$ be an arithmetic progression with $$a_1$$ = 3 and $$a_{2}$$ = 7. If $$a_1$$+ $$a_{2}$$ +...+ $$a_{3n}$$= 1830, then what is the smallest positive integer m such that m($$a_1$$+ $$a_{2}$$ +...+ $$a_n$$) > 1830?

#### Question 3

Let $$a_{1},a_{2},a_{3},a_{4},a_{5}$$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $$2a_{3}$$
If the sum of the numbers in the new sequence is 450, then $$a_{5}$$ is

#### Question 4

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

#### Question 5

An infinite geometric progression $$a_1,a_2,...$$ has the property that $$a_n= 3(a_{n+1}+ a_{n+2} + ...)$$ for every n $$\geq$$ 1. If the sum $$a_1+a_2+a_3...+=32$$, then $$a_5$$ is

## CAT 2008 Progressions and Series questions

#### Question 1

The number of common terms in the two sequences 17, 21, 25,…, 417 and 16, 21, 26,…, 466 is

## CAT 2006 Progressions and Series questions

#### Question 1

A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

#### Question 2

Consider a sequence where the $$n^{th}$$ term, $$t_n = n/(n+2), n =1, 2, ....$$ The value of $$t_3 * t_4 * t_5 * …..* t_{53}$$ equals.

## CAT 2004 Progressions and Series questions

#### Question 1

If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms?

#### Question 2

Consider the sequence of numbers $$a_1, a_2, a_3$$....... to infinity where $$a_1 = 81.33$$ and $$a_2 = -19$$ and $$a_j = a_{j-1} - a_{j-2}$$ for $$j\ge3$$. What is the sum of the first 6002 terms of this sequence?

## CAT 2003 Progressions and Series questions

#### Question 1

The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?

#### Question 2

The 288th term of the series a,b,b,c,c,c,d,d,d,d,e,e,e,e,e,f,f,f,f,f,f… is

#### Question 3

If the product of n positive real numbers is unity, then their sum is necessarily

## CAT 2002 Progressions and Series questions

#### Question 1

The nth element of a series is represented as

$$X_n = (-1)^nX_{n-1}$$
If $$X_0 = x$$ and $$x > 0$$, then which of the following is always true?

#### Question 2

Let S denotes the infinite sum $$2 + 5x + 9x^2 + 14x^3 + 20x^4 + ...$$ , where |x| < 1 and the coefficient of $$x^{n - 1}$$ is n( n + 3 )/2 , ( n = 1, 2 , . . . ) . Then S equals:

#### Question 3

A child was asked to add first few natural numbers (i.e. 1 + 2 + 3 + …) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong, the child discovered he had missed one number in the sequence during addition. The number he missed was

## CAT 2001 Progressions and Series questions

#### Question 1

For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence?

## CAT 2000 Progressions and Series questions

#### Question 1

If $$a_1 = 1$$ and $$a_{n+1} = 2a_n +5$$, n=1,2,....,then $$a_{100}$$ is equal to:

#### Question 2

What is the value of the following expression?

$$(1/(2^2-1))+(1/(4^2-1))+(1/(6^2-1))+...+(1/(20^2-1)$$

## CAT 1999 Progressions and Series questions

#### Question 1

All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?

#### Question 2

Elements of $$S1$$ are in ascending order, and those of $$S2$$ are in descending order. $$a_{24}$$ and $$a_{25}$$ are interchanged. Then, which of the following statements is true?

#### Question 3

Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than:

## CAT 1996 Progressions and Series questions

#### Question 1

First term of $$S_{1}$$ is

#### Question 2

Fourth term of $$S_{2}$$

#### Question 3

What is the difference between fourth terms of $$S_{1}$$ and $$S_{2}$$ ?

#### Question 4

What is the average value of the terms of series $$S_{1}$$?

#### Question 5

What is the sum of series $$S_{2}$$?

## CAT 1990 Progressions and Series questions

#### Question 1

What is the sum of the following series: $$\frac{1}{1 \times 2} + \frac{1}{2 \times 3}+\frac {1}{3 \times 4}$$ ....... $$+ \frac{1}{100 \times 101}$$?

#### Question 2

The value of $$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}$$

#### Question 3

Consider a function $$f(k)$$ defined for positive integers $$k = 1,2, ..$$ ; the function satisfies the condition $$f(1) + f(2) + .. = \frac{p}{p-1}$$. Where $$p$$ is fraction i.e. $$0 < p < 1$$. Then $$f(k)$$ is given by

#### Question 4

N the set of natural numbers is partitioned into subsets $$S_{1}$$ = $$(1)$$, $$S_{2}$$ = $$(2,3)$$, $$S_{3}$$ =$$(4,5,6)$$, $$S_{4}$$ = $$(7,8,9,10)$$ and so on. The sum of the elements of the subset $$S_{50}$$ is

#### Question 5

A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares such formed (in sq.cm.)is