Geometric Progressions (G.P.)

Geometric Progression (G.P.)

(a) If a is the first term r the common ratio then GP can be expressed as a, a_r, a_r2, . . ., ar_n-1

with nth term Tn = ar_n-1 = l (last term)

where with term from the last

(b) Sum of first n term

Sum of infinite GP when |r| < 1

i.e., -1 < r < 1, S∞ = |r| < 1.

(c) Geometric mean of any n positive numbers. b₁ b₂ . . . b_n is

GM = (b₁ b₂ b₃. . .

(d) If n GM’s G₁ G₂ . . . G_n are inserted between a and b, then

G_{r + 1} =