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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A certain sequence is defined by the formula an = an – 1 – 7  Question banks Downloads My Bookmarks Reviews Important topics
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Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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A certain sequence is defined by the formula an = an – 1 – 7 [#permalink]
Expert's post 00:00

Question Stats: 94% (01:10) correct 5% (02:38) wrong based on 52 sessions
A certain sequence is defined by the formula $$a_n = a_{n – 1} – 7$$.

$$a_7 = 7$$

 Quantity A Quantity B $$a_1$$ $$-35$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
_________________

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: 173

Kudos [?]: 2976  , given: 394

Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink]
1
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Expert's post
Explanation

The sequence $$a_n = a_{n - 1} - 7$$ can be read as “to get any term in sequence a, subtract 7 from the previous term.” The problem provides the 7th term; plug the term into the function in order to determine the pattern.

Note that Quantity A asks for the value of a1, so try to find the 6th term:

$$7 = a_6 - 7$$

$$a_6 = 14$$

In other words, each previous term will be 7 greater than the subsequent term. Therefore, $$a_7 = 7$$, $$a_6 = 14$$, $$a_5 = 21$$, and so on.

The term $$a_1$$, then, is greater than the starting point, 7, and must also be greater than the negative value in Quantity B. Quantity A is greater. Note that the value in Quantity B is the result of incorrectly subtracting 7 six times, rather than adding it.
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Sandy
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Manager Joined: 23 Oct 2018
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Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink]
I didnt get it Intern Joined: 22 Jul 2018
Posts: 39
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Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink]
2
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a7 = a6 - 7 = a5 - 17 = a4 -21 = a3 - 28 = a2 - 35 = a1 - 42
a7 = a1 -42
7 = a1 -42
a1 = 49
A Intern Joined: 18 May 2020
Posts: 35
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Kudos [?]: 35  , given: 2

Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink]
1
KUDOS
If you plug 7 in to solve for the 6th value in the sequence, you'll quickly start to see that with each decreasing number in the sequence, you're just adding 7 again and again.

If the values are becoming more positive and higher as you move from the 7th value to the 6th, 5th, 4th, etc., then the first value in the sequence is going to be greater than -35. You never dip into the negative numbers. So, the answer is A

It can get tricky if you subtract instead of adding. If you did that, you might end up getting answer C, which is incorrect. So, watch your signs  Re: A certain sequence is defined by the formula an = an – 1 – 7   [#permalink] 31 May 2020, 18:10
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