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The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{

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

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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Jul 2013, 11:35, edited 2 times in total.
Edited the question and moved to DS forum.

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

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New post 26 Jul 2013, 11:40
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 \(a_4\).

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

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hb wrote:
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.


Similar question to practice: a-sequence-a1-64-a2-66-a3-67-an-8-an-3-which-of-the-43871.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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.

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

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New post 04 Jan 2014, 05:26
Aurele wrote:
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.


Please read here: the-infinite-sequence-a-1-a-2-a-n-is-such-that-a-156741.html#p1250455

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?

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 08 Jan 2014, 00:45
Thanks a lot for the explanation. Don't know why I confused both.

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

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