CAT Number Series Questions & Solutions

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

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
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
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
- $\frac{15}{13}$
- $\frac{27}{12}$
- $\frac{15}{8}$
- $\frac{16}{11}$
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
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
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
- $(1003)^{15} + 6$
- $(997)^{15} - 3$
- $(997)2^{14} + 3$
- $(1003)2^{15} - 3$
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
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
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
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:
- $(2-x)/(1-x)^3$
- $(2-x)/(1+x)^3$
- $(2+x)/(1-x)^3$
- $(2+x)/(1+x)^3$
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
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

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CAT Number Series previous year questions with solutions — AthenaPrep

CAT Number Series Questions & Solutions

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

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

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

$\frac{15}{13}$
$\frac{27}{12}$
$\frac{15}{8}$
$\frac{16}{11}$

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

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

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

$(1003)^{15} + 6$
$(997)^{15} - 3$
$(997)2^{14} + 3$
$(1003)2^{15} - 3$

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

Q8.CAT 2008

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

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

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:

$(2-x)/(1-x)^3$
$(2-x)/(1+x)^3$
$(2+x)/(1-x)^3$
$(2+x)/(1+x)^3$

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

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 $S_{2}$ ?

65+ more Number Series questions inside

Get the full CAT Number Series set with timed practice, bookmarks and analysis — free to start.

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CAT Number Series previous year questions with solutions — AthenaPrep