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In a certain sequence, the term an is defined by the formula

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In a certain sequence, the term an is defined by the formula [#permalink] New post 27 Jul 2018, 01:32
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84% (00:53) correct 15% (01:44) wrong based on 39 sessions
In a certain sequence, the term an is defined by the formula \(a_n = a_{n – 1} + 10\) for each integer n ≥ 2. What is the positive difference between \(a_{10}\) and \(a_{15}\)?
(A) 5
(B) 10
(C) 25
(D) 50
(E) 100
[Reveal] Spoiler: OA

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Re: In a certain sequence, the term an is defined by the formula [#permalink] New post 12 Aug 2018, 04:48
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Explanation

This is an arithmetic sequence where the difference between successive terms is always +10.

The difference between, for example, \(a_{10}\) and \(a_{11}\), is exactly 10, regardless of the actual values of the two terms. The difference between \(a_{10}\) and \(a_{12}\) is \(10 + 10 = 20\), or \(10 \times 2 = 20\), because there are two “steps,” or terms, to get from \(a_{10}\) to \(a_{12}\). Starting from a10, there is a sequence of 5 terms to get to \(a_{15}\).

Therefore, the difference between \(a_{10}\) and \(a_{15}\) is \(10 \times 5 = 50\).
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Re: In a certain sequence, the term an is defined by the formula [#permalink] New post 06 Mar 2020, 14:04
Why don't we use inclusive counting and get 60?
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Re: In a certain sequence, the term an is defined by the formula [#permalink] New post 14 May 2020, 04:13
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a10=a9+10
a11=a9+20
a12=a9+30
a13=a9+40
a14=a9+50
a15=a9+60

Final answer: a15-a10 -> (a9+60)-(a9+10) -> a9+60-a9-10 (a9s will be canceled) -> 60-10=50
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Re: In a certain sequence, the term an is defined by the formula [#permalink] New post 31 May 2020, 18:11
If we used inclusive counting to get 60, it wouldn't be an answer choice anyway ;)
Re: In a certain sequence, the term an is defined by the formula   [#permalink] 31 May 2020, 18:11
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