Arithmetic Progressions | Class 10

 📝Class 10  Arithmetic Progression 

Arithmetic Progression (Video lectures)

What is a sequence?

What is an AP?

nth term of an AP

NCERT chapter 5, Ex 5.1

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`.

Arithmetic Series

By adding the terms of an AP, we get the corresponding arithmetic series.

Example

On adding the terms of the AP 3, 7, 11, 15, 19, ... we get the arithmetic series (3 + 7 + 11 + 15 + 19 + ...).