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

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 [0], given: 397

In a certain sequence, the term an is defined by the formula [#permalink]  27 Jul 2018, 01:32
Expert's post
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Question Stats:

57% (00:11) correct 42% (01:52) wrong based on 7 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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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 [0], given: 397

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