2. 外语
  3. Which of the following could be the units digit of 57n, where n is a positive integer? Indicate all such digits. A 0 B 1 C 2 D

Which of the following could be the units digit of 57n, where n is a positive integer? Indicate all such digits. A 0 B 1 C 2 D

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问题 Which of the following could be the units digit of 57n, where n is a positive integer?
Indicate all such digits.
A 0
B 1
C 2
D 3
E 4
F 5
G 6
H 7
I 8
J 9
选项
答案B,D,H,J
解析 The units digit of 57n is the same as the units digit of 7n for all positive integers n. To see why this is true for n = 2, compute 572 by hand and observe how its units digit results from the units digit of 72. Because this is true for every positive integer n, you need to consider only powers of 7. Beginning with n=1 and proceeding consecutively, the units digits of 7, 72, 73, 74, and 75 are 7, 9, 3, 1, and 7, respectively. In this sequence, the first digit, 7, appears again, and the pattern of four digits, 7,9, 3,1, repeats without end. Hence, these four digits are the only possible units digits of 7n and therefore of 57n.
The correct answer consists of Choices B(1), D(3), H(7), and J(9).
This explanation uses the following strategies.
Strategy 7: Find a Pattern
Strategy 12: Adapt Solutions to Related Problems
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