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# term after the first term is equal to the preceding term

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CEO
Joined: 07 Jun 2014
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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
Question: 24
Page: 336
Difficulty: easy

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Sandy
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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
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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.
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Sandy
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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
Director
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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
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
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The text passage provided is a GMAT practice question and solution for a problem involving an arithmetic sequence. The content structure includes a problem statement, a solution, and an explanation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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
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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
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user
The text passage provided is a GMAT practice question and solution for a problem involving an arithmetic sequence. The content structure includes a problem statement, a solution, and an explanation.

TYPE: SINGLE_QUESTION_WITH_ANSWER