CAT Progressions and Series Questions & Solutions

A sample of real CAT Progressions and Series past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 77 Progressions and Series questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   For any natural number k , let $a_{k}=3^{k}$. The smallest natural number m for which $\left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}<\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}$, is

   • 58

   • 59

   • 56

   • 57

2. Q2.CAT 2024

   Suppose $x_{1},x_{2},x_{3},...,x_{100}$ are in arithmetic progression such that $x_{5}=-4$ and $2x_{6}+2x_{9}=x_{11}+x_{13}$, Then,$x_{100}$ equals

   • -194

   • -196

   • 204

   • 206

3. Q3.CAT 2023

   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

   • $\frac{15}{13}$

   • $\frac{27}{12}$

   • $\frac{15}{8}$

   • $\frac{16}{11}$

4. Q4.CAT 2022

   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

   • 455

   • 442

   • 415

   • 404

5. Q5.CAT 2021

   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

   • 4849

   • 4949

   • 4950

   • 4850

6. Q6.CAT 2019

   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

   • $(1003)^{15} + 6$

   • $(997)^{15} - 3$

   • $(997)2^{14} + 3$

   • $(1003)2^{15} - 3$

7. Q7.CAT 2018

   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

   Answer: 24

8. Q8.CAT 2008

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

   • 78

   • 19

   • 20

   • 77

   • 22

9. Q9.CAT 2003

   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?

   • 1st

   • 9th

   • 12th

   • None of the above

10. Q10.CAT 2002

    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:

    • $(2-x)/(1-x)^3$

    • $(2-x)/(1+x)^3$

    • $(2+x)/(1-x)^3$

    • $(2+x)/(1+x)^3$

11. Passage

    DIRECTIONS for the following questions: These questions are based on the situation given below: There are fifty integers $a_1, a_2,...,a_{50}$, not all of them necessarily different. Let the greatest integer of these fifty integers be referred to as $G$, and the smallest integer be referred to as $L$. The integers $a_1$ through $a_{24}$ form sequence $S1$, and the rest form sequence $S2$. Each member of $S1$ is less than or equal to each member of $S2$.

    Q11.CAT 1999

    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?

    • S1 continues to be in ascending order

    • S2 continues to be in descending order

    • S1 continues to be in ascending order and S2 in descending order.

    • None of the above

12. Passage

    Answer the questions based on the following information. A series $S_{1}$ of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series $S_{2}$, the nth term is defined as the difference between the (n+1)th term and the nth term of series $S_{1}$, $S_{2}$ is an arithmetic progression with a common difference of 30.

    Q12.CAT 1996

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

    • 10

    • 20

    • 30

    • 40

CAT Progressions and Series previous year questions with solutions — AthenaPrep