Mathematics : Arithmetic Progression.

Sequence : A succession of numbers formed and arranged in a definite order according g to a certain definite rule is called a sequence.

Athematic Proration (A.P)

Arithmetic Progression (A.P) : It is a sequence in which each term , except the first one differs  from the  preceding term by a constant. This constant is called the common difference.

👉First term is denoted by a ,

👉Common difference is denoted by a  by d,

👉N^th term is denoted by a by Tn or an

👉Sum of first n term is denoted by Sn.

General Term of AP :

Example 1 : Find the 9th term from the end (towards the first term) of the A.P. 5, 9,13,185.

Solution :

Example 2 :  For what value of k will k + 9, 2k -1 and 2k + 7 are the consecutive terms of an A.P.?

Solution :

Example 3 :  For what value of k will the consecutive terms 2k + 1, 3k + 3 and 5k -1 form an A.P.?

Solution : 

Sum of Arithmetic Progression :

Sum of terms : The sum of the first n terms of an AP with initial term a and common difference d is given by

Sn​= [2a+(n−1)d]

or

 Sn​= ​[a​+an​]

or

Sn​=n×(middle term)

Example 4 :  How many terms of the A.P. 18,16,14,… be taken so that their sum is zero?

Solution :

Example 5 :  How many terms of the A.P. 27,24,21,… should be taken so that their sum is zero?

Solution :

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👉Mathematics : Arithmetic Progression.

👉Arithmetic Progression : CBSE Class 10 Important Question