Question

Să se scrie primi cinci termenii ai următoarelor progresii geometrice....

Answer 1

a) q (ratia) = b2/b1 = 3/1 = 3

b3 = b1 x q² = 1 x 3² => b3 = 9

b4 = b1 x q³ = 1 x 3³ => b4 = 27

b5 = b1 x q⁴ = 1 x 3⁴ => b5 = 81

b) q = b4/b3 = 36/24 = 6/4 = 3/2

b3 = b2 x q => 24 = b2 x 3/2 => b2 = 24 x 2/3 => b2 = 16

b2 = b1 x q =>  16 = b1 x 3/2 => b1 = 16 x 2/3 => b1 = 32/3

c) q = b4/b3 = 27/-9 = -3

b3 = b2 x q => -9 = b2 x (-3) => b2 = -9/-3 => b2 = 3

b2 = b1 x q => 3 = b1 x (-3) => b1 = 3/-3 => b1 = -1

d) b5 = b2 x q³ => 1/16 = 4 x q³ => q³ = 1/16 x 1/4 => q = V(1/64) = 1/4

b2 = b1 x q => 4 = b1 x 1/4 => b1 = 4x4 => b1 = 16

b3 = b1 x q² = 16 x 1/16 => b3 = 1

b4 = b3 x q = 1 x 1/4 => b4 = 1/4