Chapter 5 Progressions

Question

32 is the fourth term and it is half of the first term.

Answer 1

a) If this arithmetic progrssion,then: a₄ = a₁ + 3d = 32 and a₄ = 1/2a₁. So a₁ = 2a₄ = 64, 3d = a₄ - a₁ = 32 - 64 = - - 32. So d = - 32/3.

b) If this is geometric progression, then a₄ = a₁r³ = 32, a₄ = 1/2 a₁; a₁ = 2a₄ = 64; 32 = 64r³, r = (1/2)^1/3.