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A sequence of positive integers a1, a2, a3, … , an is given
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02 May 2019, 02:27
02 May 2019, 02:27
Expert Reply
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Question Stats:
77% (01:29) correct
22% (01:32) wrong based on 27 sessions
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A sequence of positive integers \(a_1\), \(a_2\), \(a_3\), … , \(a_n\) is given by the rule \(a_{n+1} = 2a_n + 1\). The only even number in the sequence is 38. What is the value of \(a_2\)?
(A) 11
(B) 25
(C) 38
(D) 45
(E) 77
(A) 11
(B) 25
(C) 38
(D) 45
(E) 77
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Joined: 09 Apr 2020
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Re: A sequence of positive integers a1, a2, a3, … , an is given
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26 Apr 2020, 18:45
26 Apr 2020, 18:45
2
Expert Reply
Carcass wrote:
A sequence of positive integers \(a_1\), \(a_2\), \(a_3\), … , \(a_n\) is given by the rule \(a_{n+1} = 2a_n + 1\). The only even number in the sequence is 38. What is the value of \(a_2\)?
(A) 11
(B) 25
(C) 38
(D) 45
(E) 77
(A) 11
(B) 25
(C) 38
(D) 45
(E) 77
For this question, use your knowledge of even and odd numbers. Although the question doesn't tell us specifically which position in the sequence the number 38 is in, we know that 2a+1 has to be an odd number. Since 38 is an even number, it has to be the first number in the sequence.
That means that the second number is 2(38) + 1 or 77.
Answer: E
Re: A sequence of positive integers a1, a2, a3, … , an is given
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31 May 2020, 18:30
31 May 2020, 18:30
3
The answer is E.
When you see 2a +1, but the question says that 38 is the only even number in the sequence, it has to be the first number in the sequence because 2a + 1 will always yield an odd number.
Therefore, the second number is 2(38) + 1 or 77.
When you see 2a +1, but the question says that 38 is the only even number in the sequence, it has to be the first number in the sequence because 2a + 1 will always yield an odd number.
Therefore, the second number is 2(38) + 1 or 77.
