Arithmetic progressions

Class 10:

• succeeding terms obtained by adding a fixed number, which is known as common difference {can be positive, negative, zero}
• each number is called as a term
• a1, a2, a3, a4, … , a(n-1), an
• a2 - a1 = a3 - a2 = an - a(n-1) = d
• a, a+d, a+2d, a+3d, … - general form of AP
• finite vs infinite AP

5.1

• which of the following form an AP
• write the first four terms of the AP
• write the first term and common difference

5.2

• nth term of the AP
• an = a + (n-1)d
• an = general term, am or l = last term
• which term is the given number?
• determine the AP
• check whether the following number comes
• find from last

5.3

• Sum of n terms in the AP
• S = n/2 (2a + (n-1)d)
• S = n/2 (a+l)
• the nth term is the difference of the sum of first n terms and the sum of first n-1 terms
• an = Sn - (Sn-1)
• Sum of first n positive integers - Sn = (n(n+1)) / 2
• find a, an, Sn, n, d