Arithmetic Progressions (A.P.)

Arithmetic Progressions (A.P.)

(a) If a is the first term and d is the common difference then AP can be written as

a, a + d, a + 2d, . . . a + (n-1) d.

with term Tn = a + (n-1) d = l (last term)

where d = T_n – T_n-1

with term from the last T_n = l – (n - 1) d

(b) Sum of first n term

and T_n = S_n – S_n-1

(c) Arithmetic mean of any n positive numbers a₁ a₂ . . . a_n is

AM =

(d) If n arithmetic means A₁ A₂ . . . A_n are inserted between a and b then

Ar = a + 1 ≤ r ≤ n and A₀ = a, A_n+1 = b.