HarveyKlaus wrote:
1/2, 1/4, 1/8, 1/16, 1/32, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
A) 0.1 < x < 1
B) 0.01 < x < 0.1
C) 0.001 < x < 0.01
D) 0.0001 < x < 0.001
E) 0.00001 < x < 0.0001
We can think of the terms as follows....
term_1 = 1/2
term_2 = (1/2)(1/2) = (1/2)²
term_3 = (1/2)(1/2)(1/2) = (1/2)³
term_4 = (1/2)(1/2)(1/2)(1/2) = (1/2)⁴
.
.
.
term_n = (1/2)(1/2)(1/2)(1/2) = (1/2)^n
So, term_10 = (1/2)¹⁰ = 1/2¹⁰ = 1/1,024
We get: 1/10,000 < 1/1,024 < 1/1,000
In other words: 0.0001 < 1/1,024 < 0.01
Answer: D
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