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
If the 3rd term in a sequence
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This is not a GMAT-worthy question. What's the source?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
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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(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.)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
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
Answer: C
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