请教GWD 11-25

dreadpower

Q25:

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

请问如何解答,我先把X₂₀=2X₁₉-1

然后就是2X₁₉-1-X₁₉= X₁₉-1

然后难道要一个一个的算出么,谢谢

jhiiool

答案是不是选A呀?

因为根据题目，X1=3, X2=2*1-1=5,X3=2*5-1=9.

X2-X1=5-3=2^1

X3-X2=9-5=2^2

.....

X20-X19=2^19