Explicit formula of 400, 100, 25, 25/4 and use it to find the 15th term

Question

Mathematics

Julien Jarvis

12 March, 00:22

Explicit formula of 400, 100, 25, 25/4 and use it to find the 15th term

+3

Answers (1)

Know the Answer?

Erik Lucas · Answer 1

The 15th term is 25/16'777,216

Step-by-step explanation:

Aₙ = Aₙ₋₁ : 4; A₁ = 400

A₂ = A₁ : 4 = 400 : 4 = 100

A₃ = A₂: 4 = 100 : 4 = 25

A₄ = A₃ : 4 = 25 : 4 = 25/4

A₅ = A₄: 4 = 25/4 : 4 = 25/4 * 1/4 = 25/16

A₆ = A₅: 4 = 25/16 : 4 = 25/16 * 1/4 = 25/64

A₇ = A₆: 4 = 25/64 : 4 = 25/64 * 1/4 = 25/256

A₈ = A₇ : 4 = 25/256 : 4 = 25/256 * 1/4 = 25/1,024

A₉ = A₈: 4 = 25/1,024 : 4 = 25/1,024 * 1/4 = 25/4,096

A₁₀ = A₉: 4 = 25/4,096 : 4 = 25/4,096 * 1/4 = 25/16,384

A₁₁ = A₁₀ : 4 = 25/16,384 : 4 = 25/16,384 * 1/4 = 25/65,536

A₁₂ = A₁₁ : 4 = 25/65,536 : 4 = 25/65,536 * 1/4 = 25/262,144

A₁₃ = A₁₂ : 4 = 25/262,144 : 4 = 25/262,144 * 1/4 = 25/1'048,576

A₁₄ = A₁₃ : 4 = 25/1'048,576 : 4 = 25/1'048,576 * 1/4 = 25/4'194,304

A₁₅ = A₁₄ : 4 = 25/4'194,304 : 4 = 25/4'194,304 * 1/4 = 25/16'777,216

The 15th term is 25/16'777,216