GWD 11 Math 25求教！！

mindfrees

If the sequence x₁, x_2, x_{3, …,} x_n, … is such that x₁ = 3 and x_n+1 = 2x_n – 1 for n ≥ 1, then x₂₀ – x₁₉ =

A. 2¹⁹

B. 2²⁰

C. 2²¹

D. 2²⁰ - 1

E. 2²¹ - 1

apple1

If the sequence x1, x2, x3, …, xn, … is such that x1 = 3 and xn+1 =

2xn – 1 for n ≥ 1, then x20 – x19 =

因为：Xn+1=2Xn -1

所以：Xn=2Xn-1 -1

两式相减，得Xn+1 - Xn=2(Xn-Xn-1)

同理可得，Xn-Xn-1=2(Xn-1-Xn-2)

……以此类推

Xn+1-Xn=2(Xn-Xn-1)=2^(n-1)*(X2-X1)，因为X2=2X1-1=6-1=5

所以Xn+1-Xn=2^n，当n=19时，选A.

A. 219

B. 220

C. 221

D. 220 - 1

E. 221 - 1