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In the sequence S, the difference between any two consecutive terms is

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In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post Updated on: 07 Aug 2018, 21:24
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A
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In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?

    A. -4
    B. 0
    C. 4
    D. 8
    E. Cannot be Determined

Thanks,
Saquib
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Originally posted by EgmatQuantExpert on 23 May 2017, 07:03.
Last edited by EgmatQuantExpert on 07 Aug 2018, 21:24, edited 1 time in total.
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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post Updated on: 31 May 2017, 04:44

Originally posted by EgmatQuantExpert on 23 May 2017, 07:03.
Last edited by EgmatQuantExpert on 31 May 2017, 04:44, edited 1 time in total.
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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post 23 May 2017, 07:09
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the sequence is in AP and the second term would be 1st term plus the common difference. Now,2a +7d = a+6d => a+ d = 0 -> option B
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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post 23 May 2017, 08:43
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Let the first seven terms be denoted as below
a,a+d,a+2d,a+3d,a+4d,a+5d,a+6d

Now,
a+3d+a+4d=a+6d
a=-d

So second term = d-d = 0

Answer is B. 0
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In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post Updated on: 07 Aug 2018, 21:26

Official Solution




Given


    • In a sequence S, difference between any two terms is equal

      o S is an arithmetic sequence
      o Let the first term of the sequence be a and the common difference be d

    • 4th   term + 5th  term = 7th  term

      o 4th  term = a + (4-1)*d = a+ 3d
      o 5th  term = a + (5-1)*d = a +4d
      o 7th term = a + (7-1)d = a + 6d

To Find: a + d = ?


Working Out

    • (a + 3d) + (a+4d) = a+ 6d

      o 2a + 7d = a + 6d

      o a + d = 0

    • Hence, the value of the 2nd term of the sequence = a + d = 0



Answer: B

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Originally posted by EgmatQuantExpert on 31 May 2017, 04:44.
Last edited by EgmatQuantExpert on 07 Aug 2018, 21:26, edited 1 time in total.
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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post 20 Jun 2017, 15:12
a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d, a+7d.

a4= a7-a5 = 2d

Therefore:
a2= a4 - d - d= 0

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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post 14 Jul 2017, 02:00
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EgmatQuantExpert wrote:
In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?

    A. -4
    B. 0
    C. 4
    D. 8
    E. Cannot be Determined

Thanks,
Saquib
Quant Expert
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A very easy question!

Use concept of AP.

a+3d + a+4d = a+6d

a+d = 0
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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post 07 Aug 2017, 00:59
a+3d+a+4d=a+6d [From problem statement]
a+d=0 -> This would be the 2nd term of the series.
Option B.
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Re: In the sequence S, the difference between any two consecutive terms is  [#permalink]

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New post 07 Aug 2017, 22:14
EgmatQuantExpert wrote:
In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence?

A. -4
B. 0
C. 4
D. 8
E. Cannot be Determined


let x+3=fourth term
x+4=fifth term
x+6=seventh term
adding, 2x+7=x+6➡
x=-1=first term
sequence=-1,0,1,2,3,4,5..
second term=0
B
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Re: In the sequence S, the difference between any two consecutive terms is   [#permalink] 07 Aug 2017, 22:14
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