Progressions and Series

The progression and series is one of the most important topics of the CAT quantitative aptitude section. In general, nearly 4-5 questions are asked every year from the topics of progression and series in the CAT paper. So, it is very crucial for the candidates to be very well prepared with the topic to be able to ace the CAT easily.

Definition and Concepts of Progressions & Series:

The progression can be defined as a number of things in a series. The progressions can be widely classified into three different types i.e.:

  • Arithmetic Progression
  • Geometric Progression and
  • Harmonic Progression

The candidates can visit the linked pages for detailed explanations on the individual types of progressions.

Illustrations: Progressions

Arithmetic Progression:

In an arithmetic progression sequence, the difference between the consecutive numbers is always constant. Visit arithmetic progression to learn more about the topic in detail.

AP Formulae:

  • nth term = a + (n – 1) d

  • Sum of n terms= (n/2) (first term + last term)

Example 1

What is the sum of the following AP?

1,3,5,7,………199

Solution:

In this series, a= 1, d=2, last term (l) = 199

Now, AP formula= a+(n-1)d= l

So, 1+(n-1)2= 199

I.e. n= 200.

Now, sum of n terms= n/2(a+l)

=> 50(1+199)

= 10000.

Geometric Progression:

In this sequence, the numbers are placed such that the ratio between each number and the preceding number is always same. To learn more from detailed explanation on the topic, visit geometric progressions.

GP Formulae:

  • nth term = ar^(n-1)

  • Sum of n terms= a ((r^n-1))/((r-1) ) (1 < r)

Example 2

What will be the eighth term of the following GP?

1/3 – 1/6 + 1/12 – 1/24

Solution:

In this GP, common ration, r= (⅓)/(-⅙) i.e. r= -½

So, eighth term = ar^7 =  (1/3) × ((-1)/2)^7 = (-1)/384.

Harmonic Progression:

The harmonic progression can simply be defined as a series in which the reciprocals are in arithmetic progression. Check the linked article to get thorough with the topic along with additional information involving harmonic mean and its applications.

HP Formula:

  • nth term =  1/((nth term of corresponding AP))

Example 3:

Find the fourth term of the given HP>

1/2, 1/5, ⅛

Solution:

The corresponding AP of the given HP is: 2,5,8.

Here common difference, d= 3.

So, fourth term of the AP is 11 which means that the fourth term of  the HP will be reciprocal to it.

Hence, the fourth term of the given HP is 1/11.

The CAT aspirants are suggested to visit some important number series to learn and completely get acquainted with important series, their applications and other related concepts. Keep visiting Byju’s to learn more such important CAT exam topics easily and get various preparation tips to effectuate the learning process.