]]>
LearnNext
Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

General Term

1,19,676 Views
Have a doubt? Clear it now.
live_help Have a doubt, Ask our Expert Ask Now
format_list_bulleted Take this Lesson Test Start Test

General Term - Lesson Summary

Sequence
A sequence is an arrangement of numbers in a definite order according to some rule.

Arithmetic Progression
There are various patterns in daily life. Arithmetic Progression in short A.P is a sequence of numbers or terms in which each term except the first term is obtained by adding a fixed number or constant to the preceding term. This constant or fixed number is called common difference denoted by d.

A sequence a 1, a 2, a 3, a 4,--------------,a n is called an arithmetic progression, if there exist a common difference d such that a 2 - a 1 = a 3 - a 2 = --------- = a n - a n-1  = d.

If the first term is a and the common difference d, then a, a + d, a + 2d, a + 3d, ----------is an arithmetic progression.

General term or nth term of A.P

The general term or n th term of A.P is given by t n = a + (n – 1)d, where a is the first term, d is the common difference and n is the number of term.

Common difference is given by  d = t 2 – t 1 = t 3 – t 2 = ……..

The n th term is also denoted with l or b.

Selection of terms in A.P
If the number of terms in A.P is 3 then the terms are assumed as a - d , a , a + d. Here d is the common difference .

If the number of terms in A.P is 4 then the terms are assumed as a - 3d , a - d , a + d , a + 3d. Here 2d is the common difference .
  
If the number of terms in A.P is 5 then the terms are assumed as a - 2d , a - d , a , a + d , a + 2d. Here d is the common difference .

If the number of terms in A.P is 6 then the terms are assumed as a - 5d , a - 3d , a - d , a + d , a + 3d , a + 5d. Here 2d is the common difference .

Note:
If three numbers a, b , c are in A.P then 2b = a + c.

If three numbers a, b , c are in A.P then b is known as the arithmetic mean between a and c.

Arithmetic mean between a and b is (a + b) 2

Comments(0)

Feel the LearnNext Experience on App

Download app, watch sample animated video lessons and get a free trial.

Desktop Download Now
Tablet
Mobile
Try LearnNext at home

Get a free home demo. Book an appointment now!

GET DEMO AT HOME