Progression and Series - QA Formulae

By BYJU'S CAT|Updated : June 12th, 2023

There are three standard types of progressions:

  1. Arithmetic progression
  2. Geometric progression
  3. Harmonic progression

Arithmetic progression (AP):

  • If the sum or difference of any two consecutive terms is constant, then the terms are said to be in AP.

For example, 3, 7, 11, 15…… or a, a + d, a + 2d, a + 3d…


If ‘a’ is the first term and ‘d’ is the common difference, then the general ‘nth’ term is given by

byjusexamprep

Table of Content

Properties of AP:

       If a, b, c, d,…. are in AP and ‘k’ is a constant then

  • a – k, b – k, c – k,… will also be in AP
  • ak, bk, ck,… will also be in AP
  • a/k, b/k, c/k will also be in AP

Geometric progression (GP)

  • If in a succession of numbers, the ratio of any term and the previous term is constant then the numbers are said to be in geometric progression.

byjusexamprep

Properties of GP:

     If a, b, c, d,…. are in GP and ‘k’ is a constant, then

  • ak, bk, ck,… will also be in GP
  • a/k, b/k, c/k,... will also be in GP

Harmonic progression (HP):

  • If a, b, c, d,... are unequal numbers then they are said to be in HP if 1/a, 1/b, 1/c,... are in AP
  • The ‘nth’ term in HP is 1/(nth term in AP)

 Properties of HP:

   If a, b, c, d,… are in HP, then

  • a + d > b + c
  • ad > bc

Standard series:

byjusexamprep

Arithmetic mean:

byjusexamprep

The final series is a, a + d, a + 2d,….

Geometric mean (GM):

byjusexamprep

 Harmonic mean:

byjusexamprep

 Relationship between AM, GM, and HM for two numbers a and b:

byjusexamprep

===========================

Download the BYJU’S Exam Prep App NOW

The most comprehensive exam prep app.

If you are aiming to crack CAT and other MBA Exam, join BYJU'S Exam Prep Online Classroom Program where you get : 

  • Live Courses by Top Faculty
  • Daily Study Plan 
  • Comprehensive Study Material 
  • Latest Pattern Test Series 
  • Complete Doubt Resolution 
  • Regular Assessments with Report Card

Comments

write a comment

Follow us for latest updates