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
