Progressions Formulas, Tricks and Shortcuts

Arithmetic Progressions Page - 2
Geometric Progressions Page - 3
Progressions Important Questions Page - 6

Sequences, following specific patterns are called progressions. Arithmetic progression (A.P). In this Chapter, besides discussing more about A.P.; arithmetic mean, geometric mean, relationship between A.M. and G.M., special series in forms of sum to n terms of consecutive natural numbers, sum to n terms of squares of natural numbers and sum to n terms of cubes of natural numbers will also be studied.

Sequences

Let the number of person’s ancestors for the first, second, third, ..., tenth generations are 2, 4, 8, 16, 32, ..., 1024. These numbers form what we call a sequence. Consider the successive quotients that we obtain in the division of 10 by 3 at different steps of division. In this process we get 3,3.3,3.33,3.333, ... and so on. These quotients also form a sequence. The various numbers occurring in a sequence are called its term . We denote the terms of a sequence by a_{1},a_{2},a_{3},.....,a_{n} etc, the subscripts denote the position of the term. The n^{th} term is the number at the position of the sequence and is denoted by a_{n} The n^{th} term is also called the general term of the sequence.

A sequence is called infinite, if it is not a finite sequence. For example, the sequence of successive quotients mentioned above is an infinite sequence, infinite in the sense that it never ends .Often, it is possible to express the rule, which yields the various terms of a sequencein terms of algebraic formula. Consider for instance, the sequence of even natural number 2, 4, 6,...
Here, a_{1}=2=2\times 1,a_{2}=4=2\times 2,a_{3}=6=2\times 3,........a_{23}=46=2\times 23,a_{24}=48=2\times 24 , and so on. In some cases, an arrangement of numbers such as 1, 1, 2, 3, 5, 8,.. has no visible pattern, but the sequence is generated by the recurrence relation given by.
a_{1}=a_{2}=1,a_{3}=a_{1}+a_{2},a_{n}=a_{n+2}+a_{n-1},n> 2
Above sequence is called Fibonacci sequence

Series

a_{1},a_{2},a_{3},.....,a_{n} be a given sequence. Then, the expression a_{1}+a_{2}+a_{3}+.....+a_{n} s called the series associated with the given sequence. The series is finite or infinite according as the given sequence is finite or infinite. Series are often represented in compact form called sigma notation as means indicating the summation involved .Thus , the series a_{1}+a_{2}+a_{3}+.....+a_{n} is abbreviated . as \sum_{k-1}^{n}

Note: When the series is used, it refers to the indicated sum not to the sum itself. For example, 1 + 3 + 5 + 7 is a finite series with four terms. When we use the phrase “ sum of a series,” we will mean the number that results from adding the terms, the
sum of the series is 16.

 

Latest Jobs

  1. Type
    Job Notification
    Job
    IBPS Recruitment Specialist Officers 1163 Vacancies - Last Date 26-11-2019
    Location
    Anywhere
    Date Posted
    20 Nov 2019
  2. Type
    Job Notification
    Job
    CISF Recruitment for 300 HEAD CONSTABLE - SPORTS QUOTA - Last Date 17-12-2019
    Location
    Anywhere
    Date Posted
    19 Nov 2019
  3. Type
    Job Notification
    Job
    IOCL Invites Application for 1542 Apprentice - Last Date 15-11-2019
    Location
    Anywhere
    Date Posted
    5 Nov 2019
  4. Type
    Job Notification
    Job
    SAIL Bhilai Recruitment of Operator cum Technician, Nurse, Fire Station Officer, and more - Last Date 15-11-2019
    Location
    Vaishali NagarChhattisgarh, India
    Date Posted
    5 Nov 2019
  5. Type
    Job Notification
    Job
    Naval Ship Repair Yard, Karnataka Recruitment of 145 ITI qualified. - Last Date 01-12-2019
    Location
    KarwarKarnataka, India
    Date Posted
    5 Nov 2019
  6. Type
    Job Notification
    Job
    IIT Dhanbad 191 Recruitment Engineers, Staff Nurse and others - Last Date 14-12-2019
    Location
    DhanbadJharkhand, India
    Date Posted
    5 Nov 2019
  7. Type
    Job Notification
    Job
    INDIAN Bank Recruitment of 115 Security Guard cum Peon – Last Date 08-11-2019
    Location
    Anywhere
    Date Posted
    28 Oct 2019
  8. Type
    Job Notification
    Job
    AIIMS Rishikesh 184 Recruitment Staff Nurse, Assistant Nursing Superintendent – Last Date 30-11-2019
    Location
    RishikeshUttarakhand, India
    Date Posted
    28 Oct 2019
  9. Type
    Job Notification
    Job
    Cement Corporation of India Recruitment of 60 Artisan Trainees - Last Date - 25-10-2019
    Location
    Anywhere
    Date Posted
    25 Oct 2019
  10. Type
    Job Notification
    Job
    MFL Recruitment of 93 Engineering, Management Trainees, Assistant Trainees - Last Date 25-10-2019
    Location
    ChennaiTamil Nadu, India
    Date Posted
    25 Oct 2019

Jobs by Category

Syllabus and Previous Papers

Leave a Reply

Your email address will not be published. Required fields are marked *