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TAGS: Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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In a certain sequence, the term an is defined by the formula [#permalink]
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Expert's post 00:00

Question Stats: 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

_________________

Sandy
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Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2922  , given: 394

Re: In a certain sequence, the term an is defined by the formula [#permalink]
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Expert's post
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 $$10 \times 5 = 50$$.
_________________

Sandy
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Manager Joined: 02 Mar 2020
Posts: 55
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Kudos [?]: 7 , given: 2

Re: In a certain sequence, the term an is defined by the formula [#permalink]
Why don't we use inclusive counting and get 60? Intern  Joined: 07 May 2020
Posts: 20
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Kudos [?]: 12  , given: 62

Re: In a certain sequence, the term an is defined by the formula [#permalink]
1
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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
Intern Joined: 18 May 2020
Posts: 35
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Kudos [?]: 30 , given: 2

Re: In a certain sequence, the term an is defined by the formula [#permalink]
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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