In the sequence S, the difference between . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

In the sequence S, the difference between . . .

by Vincen » 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.

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Source: Beat The GMAT — Problem Solving | Tue Dec 05, 2017 9:19 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » 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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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » 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 hope this explanation may help you.

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

Regards.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » 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.

Answer: B

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