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## In the sequence S, the difference between . . .

tagged by: Vincen

This topic has 2 expert replies and 1 member reply

### Top Member

Vincen Legendary Member
Joined
07 Sep 2017
Posted:
561 messages
6

#### In the sequence S, the difference between . . .

Tue Dec 05, 2017 9:19 am
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

The OA is B.

Why is B the correct answer? How can I determine this value? I need your help experts.

Thanks.

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
792 messages
Followed by:
3 members
43
Thu Jan 11, 2018 4:42 pm
Vincen 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
We can let the first term = x.

The second term is x + n.

The 3rd is x + 2n.

The 4th is x + 3n.

The 5th is x + 4n.

The 6th is x + 5n.

The 7th is x + 6n.

Thus:

x + 3n + x + 4n = x + 6n

2x + 7n = x + 6n

x = -n

So, the 2nd term is -n + n = 0.

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Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

EconomistGMATTutor GMAT Instructor
Joined
04 Oct 2017
Posted:
545 messages
Followed by:
10 members
180
Tue Dec 05, 2017 10:40 am
Hello Vincen.

We have that the difference between any two consecutive terms is equal, that is to say, $$S=a,\ \ a+d,\ \ a+2d,\ \ a+3d,\ \ a+4d,\ \ a+5d,\ \ a+6d\ .\ .\ .\ .$$ Also we have that the sum of the fourth term and the fifth term of the sequence is equal to the seventh term, that is to say, $$\left(a+3d\right)+\left(a+4d\right)=a+6d\ \leftrightarrow\ 2a+7d=a+6d\ \leftrightarrow\ \ a=-d.$$ Replacing this value of "a" in the second term of the sequence we will get $$a+d=-d+d=0.$$ So, the correct answer is B.

I'm available if you'd like a follow up.

Regards.

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### Top Member

regor60 Master | Next Rank: 500 Posts
Joined
15 Oct 2009
Posted:
236 messages
27
Tue Dec 05, 2017 9:39 am
Vincen 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

The OA is B.

Why is B the correct answer? How can I determine this value? I need your help experts.

Thanks.
Call the first number in the sequence N. The problem states that consecutive terms differ by a constant amount, call it X.

So the first number in the sequence is N. The second N+X and so on, with fourth term being N+3X, fifth being N+4X and seventh being N+6X.

The problem states that the sum of fourth and fifth terms equals seventh term, so:

(N+3X)+(N+4X) = N+6X

simplifying 2N+7X=N+6X yields X=-N

Looks strange but continue with that and substitute back into the second sequence term above

N+X = N+(-N) =
0, B

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