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605-655 (Medium)|   Algebra|   Sequences|      
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In the sequence S, the difference between any two consecutive terms is Updated on: 07 Aug 2018, 21:24
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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68% (01:53) correct 32% (02:16) wrong based on 1147 sessions

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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

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B
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quantumliner
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In the sequence S, the difference between any two consecutive terms is 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 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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The official solution has been posted. Looking forward to a healthy discussion..:)
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In the sequence S, the difference between any two consecutive terms is 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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In the sequence S, the difference between any two consecutive terms is Updated on: 07 Aug 2018, 21:26
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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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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In the sequence S, the difference between any two consecutive terms is 20 Jun 2017, 15:12
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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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In the sequence S, the difference between any two consecutive terms is 14 Jul 2017, 02:00
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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

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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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In the sequence S, the difference between any two consecutive terms is 07 Aug 2017, 00:59
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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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In the sequence S, the difference between any two consecutive terms is 07 Aug 2017, 22:14
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EgmatQuantExpert
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
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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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In the sequence S, the difference between any two consecutive terms is 16 Apr 2026, 05:50
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Deconstructing the Question

Since the difference between consecutive terms is constant, the sequence is arithmetic.

Let the first term be \(a\) and the common difference be \(d\).

Then the \(n\)th term is

\(T_n=a+(n-1)d\)

We are given that

\(T_4+T_5=T_7\)

and we need to find \(T_2\).

Step-by-step

Write the relevant terms:

\(T_4=a+3d\)

\(T_5=a+4d\)

\(T_7=a+6d\)

Use the condition:

\((a+3d)+(a+4d)=a+6d\)

Simplify:

\(2a+7d=a+6d\)

\(a+d=0\)

But

\(T_2=a+d\)

So

\(T_2=0\)

Answer: B
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In the sequence S, the difference between any two consecutive terms is 26 Apr 2026, 11:40
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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


This question says that the difference between any 2 terms is equal

That means 2nd term - 1st term = 3rd term - 2nd term = nth term - (n-1)th term

This means that we have a sequence in A.P. (Arithmetic Progression)

In an A.P.,nth term = a + (n-1)d

a= 1st term
d= difference between each term

We can form a sequence now: a, a+d, a+2d, a+3d ....

4th term: a + (4-1)d = a+3d

5th term: a+4d

7th term: a+6d

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

a = -d

Substitute -d into the 2nd term of our A.P.

-d +d = 0

That means my answer is :

B
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