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.
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Year | Weightage |
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.
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 articles 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. 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), ….. 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
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
correct answer:-2
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
correct answer:-4
If $$a_1 + a_2 + a_3 + .... + a_n = 3(2^{n + 1} - 2)$$, for every $$n \geq 1$$, then $$a_{11}$$ equals
correct answer:-6144
If $$(2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280$$, then whatis the value of $$1 + 2 + 3 + .. + n?$$
correct answer:-4851
The number of common terms in the two sequences: 15, 19, 23, 27, . . . . , 415 and 14, 19, 24, 29, . . . , 464 is
correct answer:-2
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
correct answer:-24
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
correct answer:-3
The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is
correct answer:-80707
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
correct answer:-105
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
correct answer:-3
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
correct answer:-1
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?
correct answer:-2
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
correct answer:-51
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
correct answer:-1
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
correct answer:-3
The number of common terms in the two sequences 17, 21, 25,…, 417 and 16, 21, 26,…, 466 is
correct answer:-3
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?
correct answer:-4
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.
correct answer:-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?
correct answer:-1
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?
correct answer:-3
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?
correct answer:-3
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
correct answer:-4
If the product of n positive real numbers is unity, then their sum is necessarily
correct answer:-3
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?
correct answer:-4
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:
correct answer:-1
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
correct answer:-4
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?
correct answer:-3
If $$a_1 = 1$$ and $$a_{n+1} = 2a_n +5$$, n=1,2,....,then $$a_{100}$$ is equal to:
correct answer:-4
What is the value of the following expression?
$$(1/(2^2-1))+(1/(4^2-1))+(1/(6^2-1))+...+(1/(20^2-1)$$
correct answer:-3
All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?
correct answer:-4
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?
correct answer:-1
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:
correct answer:-4
First term of $$S_{1}$$ is
correct answer:-3
Fourth term of $$S_{2}$$
correct answer:-1
What is the difference between fourth terms of $$S_{1}$$ and $$S_{2}$$ ?
correct answer:-2
What is the average value of the terms of series $$S_{1}$$?
correct answer:-3
What is the sum of series $$S_{2}$$?
correct answer:-2
What is the sum of the following series: $$ \frac{1}{1 \times 2} + \frac{1}{2 \times 3}+\frac {1}{3 \times 4}$$ ....... $$+ \frac{1}{100 \times 101}$$?
correct answer:-3
The value of $$\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^4}$$
correct answer:-1
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
correct answer:-1
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
correct answer:-4
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
correct answer:-1