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A certain sequence is defined by the formula an = an – 1 – 7

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A certain sequence is defined by the formula an = an – 1 – 7 [#permalink] New post 30 Jul 2018, 10:28
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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.
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Retired Moderator
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Kudos [?]: 2976 [1] , given: 394

Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink] New post 12 Aug 2018, 05:41
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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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Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink] New post 25 Oct 2018, 04:37
I didnt get it
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Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink] New post 31 Oct 2018, 00:51
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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
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Re: A certain sequence is defined by the formula an = an – 1 – 7 [#permalink] New post 31 May 2020, 18:10
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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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A certain sequence is defined by the formula an = an – 1 – 7

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