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The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]

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26 Jul 2013, 11:09

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The infinite sequence \(a_{1}\), \(a_{2}\), …, \(a_{n}\), … is such that \(a_{1} = 7\), \(a_{2} = 8\), \(a_{3} = 10\), and \(a_n=a_{n-3} + 7\) for values of n > 3. What is the remainder when \(a_{n}\) is divided by 7?

(1) n is a multiple of 3. (2) n is an even number.

Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question.

Source: Veritas Prep; Book 04 Chapter: Homework Topic: Algebra Question: 94 Question: Page 227 Edition: Third

My Question: Please provide an explanation on how to arrive at the answer.

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Last edited by Bunuel on 26 Jul 2013, 11:35, edited 2 times in total.

The infinite sequence \(a_{1}\), \(a_{2}\), …, \(a_{n}\), … is such that \(a_{1} = 7\), \(a_{2} = 8\), \(a_{3} = 10\), and \(a_n=a_{n-3} + 7\) for values of n > 3. What is the remainder when \(a_{n}\) is divided by 7?

\(a_{1} = 7\) \(a_{2} = 8\) \(a_{3} = 10\) \(a_{4} = a_1+7=7+7=14\) \(a_{5} = a_2+7=8+7=15\) \(a_{6} = a_3+7=10+7=17\) ... Notice that the remainder upon division the above terms by 7 repeats in blocks of 3: {0, 1, 3} {0, 1, 3}...

(1) n is a multiple of 3 --> every third term has the remainder of 3 (\(a_{3}\), \(a_{6}\), \(a_{9}\), ...). Sufficient.

(2) n is an even number. Not sufficient: consider \(a_2\) and \(a_4\).

The infinite sequence \(a_{1}\), \(a_{2}\), …, \(a_{n}\), … is such that \(a_{1} = 7\), \(a_{2} = 8\), \(a_{3} = 10\), and \(a_n=a_{n-3} + 7\) for values of n > 3. What is the remainder when \(a_{n}\) is divided by 7?

(1) n is a multiple of 3. (2) n is an even number.

Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question.

Source: Veritas Prep; Book 04 Chapter: Homework Topic: Algebra Question: 94 Question: Page 227 Edition: Third

My Question: Please provide an explanation on how to arrive at the answer.

Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]

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03 Jan 2014, 15:25

Hey,

I don't get how the OA can be A. Can anyone please explain?

As per my understanding the OA should be E:

Statement 1 says "n is a multiple of 3."

By applying the formula given in the question stem, we can find that a5=15 and that a7=21. Yet, 15 divided by 7 gives a remainder of 1, while 21 divided by 7 gives a remainder of 0. Hence, IMO statement 1 is insufficient.

Statement 2 says "n is an even number".

Also insufficient: a2=8 gives a remainder of 1, while a4=14 gives a remainder of 0.

Statements 1 and 2 combined say "n is a multiple of 3 and n is an even number".

IMO insufficient. For instance, a9=24 and a14=36. Both are multiples of 3 and are even. However, the former result gives a remainder of 3 whereas the latter one gives a remainder of 1.

Is there something that I'm misunderstanding? Please advise.

I don't get how the OA can be A. Can anyone please explain?

As per my understanding the OA should be E:

Statement 1 says "n is a multiple of 3."

By applying the formula given in the question stem, we can find that a5=15 and that a7=21. Yet, 15 divided by 7 gives a remainder of 1, while 21 divided by 7 gives a remainder of 0. Hence, IMO statement 1 is insufficient.

Statement 2 says "n is an even number".

Also insufficient: a2=8 gives a remainder of 1, while a4=14 gives a remainder of 0.

Statements 1 and 2 combined say "n is a multiple of 3 and n is an even number".

IMO insufficient. For instance, a9=24 and a14=36. Both are multiples of 3 and are even. However, the former result gives a remainder of 3 whereas the latter one gives a remainder of 1.

Is there something that I'm misunderstanding? Please advise.

We need to find the remainder when when \(a_{n}\) is divided by 7. (1) says n is a multiple of 3. Why are you checking the remainder when \(a_5\) or \(a_7\) is divided by 7. Is 5 or 7 a multiple of 3?

Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]

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11 Oct 2017, 10:08

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