Summary

An arithmetic progressionÂ (A.P)Â is a list of numbers in which difference between two consecutive numbersÂ (except the first term) is called theÂ Common Difference (d)Â and is always equal.Â A sequenceÂ a_{1},Â a_{2},Â a_{3},â€¦Â is said to be an Arithmetic Progression ifÂ aÂ _{n}Â _{+1}Â â€“Â a_{n}Â =Â constant for allÂ nÂ ÃŽÂ N.Â The General form of an A. P. isÂ a,Â aÂ +Â d,Â aÂ + 2Â d,Â aÂ + 3Â d, â€¦

In an A. P. with first termÂ aÂ and common differenceÂ d, the nth term otherwise called as â€˜General Termâ€™ is given byÂ a_{n}Â =Â aÂ + (nÂ â€“ 1)Â d.

If â€˜lâ€™ is the last term of an A. P.,Â aÂ is the first term and â€˜dâ€™ the common difference, then the number of termsÂ nÂ =Â .

The sum of the first
 nÂ terms of an AP given by Â S_{Â n}Â =Â

 Also ifÂ lÂ is the last term of a finite AP (or) theÂ nth term, then the sum of all terms of an AP is given by:Â
(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 nonzero constant, another AP is formed.Â S_{n}Â =Â