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## If the 3rd term in a sequence

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BTGmoderatorRO Moderator
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#### If the 3rd term in a sequence

Sat Feb 17, 2018 3:58 pm
If the 3rd term in a sequence is 25 and the 10th term is - 3. what is the 87th term in the sequence

(A)15
(B)299
(C)-311
(D)- 354
(E)-408

OA is C
Can an Expert help me with the formula here? Thanks

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Sat Feb 17, 2018 7:04 pm
Roland2rule wrote:
If the 3rd term in a sequence is 25 and the 10th term is - 3. what is the 87th term in the sequence

(A)15
(B)299
(C)-311
(D)- 354
(E)-408

OA is C
Can an Expert help me with the formula here? Thanks
This is not a GMAT-worthy question. What's the source?

We have no information about this sequence to help us be certain of the value of the 87th term.
In fact, the sequence COULD be as follows: 25, -3, 25, -3, 25, -3, 25, -3, 25, -3,.... [notice that the 3rd term is 25 and the 10th term is -3]
In this case, the 87th term is 25 (not among the answer choices)

Or, of course, the sequence could have a totally different pattern, in which case the answer is something else.

Cheers,
Brent

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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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Thu Feb 22, 2018 4:59 pm
Roland2rule wrote:
If the 3rd term in a sequence is 25 and the 10th term is - 3. what is the 87th term in the sequence

(A)15
(B)299
(C)-311
(D)- 354
(E)-408
(Note: The problem doesn’t say what kind of sequence it is, but let’s assume that it is an arithmetic sequence since by looking at the answer choices, it seems to suggest the sequence is an arithmetic one.)

Recall that the nth term, a_n, of an arithmetic sequence is given by the formula: a_n = a_1 + d(n - 1), where a_1 is the first term and d is the common difference. Another useful formula we can use (especially when two terms, a_m and a_k, are given) is: a_m = a_k + d(m - k).

Since the 3rd term is 25 and the 10 term is -3, by letting m = 10 and k = 3, we can use the second formula to say:

-3 = 25 + d(10 - 3)

-28 = 7d

-4 = d

Use the second formula again, now letting m = 87 and k = 3 with d = -4, we have:

a_87 = 25 + (-4)(87 - 3)

a_ 87 = 25 - 336

a_87 = - 311

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