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  • An arithmetic progression (A.P) is a list of numbers in which difference between two consecutive numbers  (except the first term) is called the Common Difference (d) and is always equal. A sequence a1a2a3,… is said to be an Arithmetic Progression if n +1 – an = constant for all n Î N. The General form of an A. P. is aa + da + 2 da + 3 d, …

  • In an A. P. with first term a and common difference d, the nth term otherwise called as ‘General Term’ is given by an = a + (n – 1) d.

  • If ‘l’ is the last term of an A. P., a is the first term and ‘d’ the common difference, then the number of terms n = .

    • The sum of the first

    • n terms of an AP given by  S n = 
  • Also if l is the last term of a finite AP (or) the nth term, then the sum of all terms of an AP is given by: 
A few properties of an AP

(i) If a constant quantity is added to or subtracted from each term of a given AP, we get another AP.

(ii) If each term of a given AP is multiplied or divided by a non-zero constant, another AP is formed. Sn = 

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