Geometric Progression

Geometric progression example question:

1. write down the first five terms of the geometric progression which has first term 1 and common ratio ½

Answer:

              1^½, ½^½, ¼^½, ⅙^½, ⅛^½, 

2. find the 10th and 20th terms of the GP with first term 3 and common ratio 2.

Answer:

10th

u_n = ar ^n-1

u₁₀ = 3 x (12) ^10-1

u₁₀ = 3 x (12) ⁹

u₁₀ = 3 x 512

u₁₀ = 1536 

20th

u₂₀ = 3 x (2) ^20-1

u₂₀ = 3 x (2) ¹⁹

u₂₀ = 1572.864

3. find the 7th term of the GP 2, -6, 18

Answer:

u_n = ar ^n-1

u₇ = 2 x (-3) ^7-1

u₇ = 2 x (-3) ⁶

u₇ = 1456