Arithmetic Progression

Arithmetic Progression

1. General form of AP

   • a, a+d, a+2d, a+3d,...a+(n-1)d

2. Sum of first n terms of AP

   • When first term and common difference are given:Sn=n/2{2a+(n-1)d} where d-Common difference
   • When first & lat terms are given: Sn=n/2(a+an) or Sn=n/2(a+l) where an-nth terms, n-total terms, l-last term

3. Definition

   • List of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term. Fixed number is called common difference

4. Arithmetic mean

   • If a, b, c, are in AP, b= (a+c)/2, b is arithmetic mean

5. Examples

   • Sum of first n positive integers Let Sn= 1+2+3+.....n a=1, last term l=n, Sn=n(a+l)/2 = n(1+n)/2

6. nth term

   • From beginning, an= a+(n-1)d Here a- first term, d-common difference, an-nth term
   • From the end an= l-(n-1)d here l- last term, d- common differnce

7. Common difference

   • i.Fixed number in arithmetic progression which provides the to & fro terms by adding/ subtracting from the present number ii.Can be positive or negative