70+ CAT Progressions Questions PDF With Video 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. 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. You can check out these CAT Progression and Series Questions PDF from the CAT previous 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.

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CAT Progressions And Series Weigthage Over Past 5 Years

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. These are one of the important topics for CAT and to avoid missing any similar important topics, checking with the CAT exam syllabus is advised.

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. Some of the concepts of Progressions are complex and getting yourself enrolled in a CAT online coaching will help you have a better control and understanding. 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)