If the 3rd term in a sequence

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

Answer: C