We’re going to learn about one particular sequence and series branch, i.e. Progression and its principles in relation. With some easy but really strong ideas, when it comes to progression, one can cut down on a lot of work. Anchoring a progression around the middle term, for example, can be very useful.

In general, from the topics of progression and series in CAT, XAT, GMAT, SNAP, NMAT, and other exams report, approximately 2-3 questions asked each year. To be able to easily ace these entrance tests, it is therefore very important for the candidates to be well prepared for the subject. Some of the exam Progression and Series questions can be very difficult and time-consuming, while others can be very easy. This section’s trick is to quickly work out whether or not a topic is solvable and not to waste time on very complicated issues.

Year | No of Questions | Good attempt | Difficulty | |

2019 | Slot 1 | 3 | 2 | Moderate |

Slot 2 | – | – | – | |

2018 | Slot 1 | 2 | 2 | Easy |

Slot 2 | 4 | 2 or 3 | Difficult |

__XAT :__

Year | No of Questions | Good attempt | Difficulty |

2020 | 2 | 2 | Easy |

2019 | 2 | 1 | Moderate |

__SNAP : __

Year | No of Questions | Good attempt | Difficulty |

2019 | 3 | 3 | Easy |

2018 | 3 | 3 | Easy |

Important concepts of sequence and progression:

- Arithmetic Progression (A.P.) – If the difference in a sequence of two consecutive terms is constant, then the sequence is called an arithmetic sequence or a progression of arithmetic
- Geometric Progression (G.P.) – If the elements of a sequence are such that they can be produced by multiplying a certain number of the previous term, it is called a geometric sequence
- Harmonic Progression (H.P.) – If we have a series and if the reciprocals of the series’ terms form an arithmetic progression, the sequence is called Harmonic Progression

Q1: The sum of the first 25 terms in AP is 525, the sum of the next 25 terms is 725, what is the common difference? (CAT 2017 – Slot 1)

1. 8/25

2. 4/25

3. 6/25

4. 1/25

1. 24

2. 30

3. 26

4. 20

Q3: Three positive numbers form an increasing GP. If the middle term of the GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is (CAT 2014 – Slot 2)

1. √2+√3

2. 3+√3

3. 2−√3

4. 2+√3

Q4: The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is (CAT 2015 – Slot 1)

1. –4

2. –12

3. 12

4. 4

Q5: The internal angles of a convex polygon are in arithmetic progression with a common difference of 10 degrees. If the smallest angle is 100 degrees, what is the number of sides of the polygon? (CAT 2017 – Slot 1)

1. 10

2. 7

3. 8

4. 9

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**Level 1 –**

It will help to minimize the time taken to solve relevant questions in CAT by keeping these Tricks & Tips for Progression and Sequence in mind. Let yourself learn the basic concepts and tricks in geometry for calculation so that you can apply them to questions quickly.

There is a chance that the questions that will come in the exam will direct questions based on the concept and hence it is advised to have clarity on basic concepts of Series and Progression.

**Level 2 –**

Write down the formulas on a sheet of paper and put them on the wall so you can see them regularly. It’ll help memorize them for you.

Questions centered on the combination of A.P and G.P, etc., may also include comprehension of other math principles such as trigonometry, logarithmic, geometry, etc. If you do not prepare this definition extensively, you will be clueless on how to proceed in the exam. Therefore, to build and learn the application of progression, you need to practice several questions.

**Level 3 –**

Including all the above levels make sure you go through all the different Progression questions from the previous years of different exams, since so many questions are based on the concepts that have appeared in previous entrance exams. Spend lots of time per day to practice quantitative aptitude in general and measurement for the entrance test you intend to appear in particular. The more time you spend on the questions, the more familiar they’ll get.

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