Class 10 Arithmetic Progression

 📝Class 10  Arithmetic Progression 

Sequence 

Some numbers arranged in a definite order, according to a definite rule, are said to form a sequence.  

The number occurring at the `nth` place of a sequence is called its `nth` term, denoted by `T_n` or `a_n`.

Example    Consider the rule,  `T_n = (2n +1)`

putting `n = 1, 2, 3, 4, 5.....` we get 

`T_1 = 3,  T_2 = 5, T_3 = 7, T_4 = 9, T_5 = 11`

Thus, the numbers 3, 5, 7, 9, 11,.... form a sequence.

In this sequence, the first term is 3, the second term is 5, and so on.

Arithmetic Progression

An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number `d` to the preceding term, except the first term. The fixed number `d` is called the common difference. The general form of an AP is `a, a + d, a + 2d, a + 3d`, . . .

➤ A sequence `a_1,  a_2,  a_3`, ....is an AP,  if the differences  `a_2 - a_1= a_3 - a_2 = a_4 - a_3= d`  

i.e.,  if `a_{k+ 1} - a_k = d`, for different values of   `k`.