Notes On General Term - CBSE Class 10 Maths
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 a1, a2, a3, a4,--------------,an is called an arithmetic progression, if there exist a common difference d such that a2 - a1 = a3 - a2 = --------- = an - an-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 nth term of A.P is given by tn = 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 = t2 – t1 = t3 – t2 = ……..

The nth 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

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 a1, a2, a3, a4,--------------,an is called an arithmetic progression, if there exist a common difference d such that a2 - a1 = a3 - a2 = --------- = an - an-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 nth term of A.P is given by tn = 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 = t2 – t1 = t3 – t2 = ……..

The nth 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

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