Added by Nitin on September 20, 2001 at 03:14:00:
Arithmetic Progression (AP)
t(n) is the general formula of each term
a is the first term of the AP
l is the last term of an AP
n denotes the number of terms
S(n) is the sum of n terms of an AP
d is the common difference between 2 consecutive terms. D must be independant of n
T(n) and S(n) are written as Tn and Sn (n- subscript)
Tn = a + (n-1)*d
d = T(n+1) - T(n)
T(m+n) - T(m-n) = 2T(m)
S(n) = (n/2)*[2a+ (n-1)d]
= (n/2)*(a + l)
T(n) = S(n+1) - S(n)
If x,y,z are three consecutive terms in an AP, then y-d=x , z-d=y. So,
2y = x + z