Question

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

Answer 1

Answer:

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