text: It is currently 14 Dec 2017, 20:23
  
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  # term after the first term is equal to the preceding term
  
  Author Message
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  term after the first term is equal to the preceding term [#permalink]  18 Jan 2016, 02:25
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  a1, a2, a3 ................ an
  
  In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If a1+a3+a5=27, what is the value of a2+a4 ?
  
  a2+a4=
  
  Practice Questions
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  Sandy
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  CEO
  Joined: 07 Jun 2014
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  GRE 1: 323 Q167 V156
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  Followers: 49
  
  Kudos [?]: 836 [2] , given: 146
  
  Re: term after the first term is equal to the preceding term [#permalink]  18 Jan 2016, 04:52
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  Solution
  
  This is clearly an arithmetic progression and we just need the first 5 terms. We can rewrite the progression as a - 2c, a - c, a , a + c, a + 2c. Here the difference between the terms is c as described in the problem
  
  a1 + a3 + a5 = a - 2c + a + a+ 2c = 3a = 27. Hence a =9.
  
  To find a2 + a4 = a - c + a + C = 2a =18.
  
  The purpose of writing this series in the above form is to eliminate c as a variable. Hence answer is 18.
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  Re: term after the first term is equal to the preceding term [#permalink]  30 Mar 2016, 09:05
  i don't understand where you derive a - 2c and a + 2c from
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  Re: term after the first term is equal to the preceding term [#permalink]  01 Apr 2016, 02:30
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  Lets take a real arithmetic progression:
  
  1, 5, 9 , 13, 17
  
  As you can see any term of the above arithmetic progression is 4 greater than the previous term. 1+4 = 5... 5+4 = 9.... so on
  
  So if we draw parallels with the question above here c = 4. Then we can write the above series taking the middle term 9 into account:
  9-2*4, 9-4, 9 , 9+4, 9+2*4
  a-2*c, a-c , a , a+c, a+2*c
  
  Thats how Sandy derives the a+2c and a-2c terms
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  Re: term after the first term is equal to the preceding term [#permalink]  29 Jun 2017, 20:10
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  If that is confusing then, you can say a, a+c, a+2c, a+3c, a+4c
  
  a1+a3+a5 = 27
  
  a + a+2c + a+4c = 27
  a = 9-2c
  
  now a2 + a4
  
  a+c + a+3c
  2a+4c
  2(9-2c) + 4c
  18-4c+4c
  
  Re: term after the first term is equal to the preceding term   [#permalink] 29 Jun 2017, 20:10
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explanation: The text extract contains a math question and an answer to the question. The question is about an arithmetic sequence where each term after the first is equal to the preceding term plus a constant \(c\). The specific question is to find the value of \(a2 + a4\) given that \(a1 + a3 + a5 = 27\).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: It is currently 14 Dec 2017, 20:23
  
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  # term after the first term is equal to the preceding term
  
  Author Message
  TAGS:
  CEO
  Joined: 07 Jun 2014
  Posts: 2910
  GRE 1: 323 Q167 V156
  WE: Business Development (Energy and Utilities)
  Followers: 49
  
  Kudos [?]: 836 [1] , given: 146
  
  term after the first term is equal to the preceding term [#permalink]  18 Jan 2016, 02:25
  1
  KUDOS
  Expert's post
  00:00
  
  Difficulty:
  
  5% (low)
  
  Question Stats:
  
  0% (00:00) correct 0% (00:00) wrong based on 0 sessions
  a1, a2, a3 ................ an
  
  In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If a1+a3+a5=27, what is the value of a2+a4 ?
  
  a2+a4=
  
  Practice Questions
  Question: 24
  Page: 336
  Difficulty: easy
  
  _________________
  
  Sandy
  If you found this post useful, please let me know by pressing the Kudos Button
  
  Try our free Online GRE Test
  
  CEO
  Joined: 07 Jun 2014
  Posts: 2910
  GRE 1: 323 Q167 V156
  WE: Business Development (Energy and Utilities)
  Followers: 49
  
  Kudos [?]: 836 [2] , given: 146
  
  Re: term after the first term is equal to the preceding term [#permalink]  18 Jan 2016, 04:52
  2
  KUDOS
  Expert's post
  Solution
  
  This is clearly an arithmetic progression and we just need the first 5 terms. We can rewrite the progression as a - 2c, a - c, a , a + c, a + 2c. Here the difference between the terms is c as described in the problem
  
  a1 + a3 + a5 = a - 2c + a + a+ 2c = 3a = 27. Hence a =9.
  
  To find a2 + a4 = a - c + a + C = 2a =18.
  
  The purpose of writing this series in the above form is to eliminate c as a variable. Hence answer is 18.
  _________________
  
  Sandy
  If you found this post useful, please let me know by pressing the Kudos Button
  
  Try our free Online GRE Test
  
  Intern
  Joined: 28 Mar 2016
  Posts: 11
  Followers: 0
  
  Kudos [?]: 0 [0], given: 0
  
  Re: term after the first term is equal to the preceding term [#permalink]  30 Mar 2016, 09:05
  i don't understand where you derive a - 2c and a + 2c from
  Director
  Joined: 16 May 2014
  Posts: 597
  GRE 1: 326 Q165 V161
  Followers: 72
  
  Kudos [?]: 313 [1] , given: 64
  
  Re: term after the first term is equal to the preceding term [#permalink]  01 Apr 2016, 02:30
  1
  KUDOS
  Expert's post
  Lets take a real arithmetic progression:
  
  1, 5, 9 , 13, 17
  
  As you can see any term of the above arithmetic progression is 4 greater than the previous term. 1+4 = 5... 5+4 = 9.... so on
  
  So if we draw parallels with the question above here c = 4. Then we can write the above series taking the middle term 9 into account:
  9-2*4, 9-4, 9 , 9+4, 9+2*4
  a-2*c, a-c , a , a+c, a+2*c
  
  Thats how Sandy derives the a+2c and a-2c terms
  _________________
  
  My GRE Resources
  Free GRE resources | GRE Prep Club Quant Tests
  If you find this post helpful, please press the kudos button to let me know !
  
  Intern
  Joined: 26 May 2017
  Posts: 5
  Followers: 0
  
  Kudos [?]: 3 [1] , given: 6
  
  Re: term after the first term is equal to the preceding term [#permalink]  29 Jun 2017, 20:10
  1
  KUDOS
  If that is confusing then, you can say a, a+c, a+2c, a+3c, a+4c
  
  a1+a3+a5 = 27
  
  a + a+2c + a+4c = 27
  a = 9-2c
  
  now a2 + a4
  
  a+c + a+3c
  2a+4c
  2(9-2c) + 4c
  18-4c+4c
  
  Re: term after the first term is equal to the preceding term   [#permalink] 29 Jun 2017, 20:10
  Display posts from previous: Sort by
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract contains a math question and an answer to the question. The question is about an arithmetic sequence where each term after the first is equal to the preceding term plus a constant \(c\). The specific question is to find the value of \(a2 + a4\) given that \(a1 + a3 + a5 = 27\).
  
  Label: question-and-answer