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

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

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

The general term or n

Common difference is given by d = t

The n

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 .

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 $\frac{\text{(a + b)}}{\text{2}}$

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

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

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

The general term or n

Common difference is given by d = t

The n

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 .

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 $\frac{\text{(a + b)}}{\text{2}}$