If sequence S has 120 terms…
We are given that sequence S has 120 terms and we must determine the 105th term of S.
Statement One Alone:
The first term of S is −8.
Without knowing anything about sequence S, other than that the first term is -8, we do not have enough information to determine the 105th term of S. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
Each term of S after the first term is 10 more than the preceding term.
Statement two gives us an indication that the sequence is an arithmetic sequence, with a common difference of 10. However, we do not know the value of any term of the sequence, and so we cannot determine the value of the 105th term. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two we know that the first term of S is −8 and that each after the first term is 10 more than the preceding term. In other words, this is an arithmetic sequence where the nth term 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. Here, a_1 = -8 and d = 10; thus, we can determine the value of each term of S and the value of the 105th term of S. Although we don’t need to find the actual value of the 105th term, we will complete the calculations as follows:
a_n = a_1 + d(n – 1)
a_105 = -8 + 10(105 – 1)
a_105 = -8 + 10(104)
a_105 = -8 + 1040
a_105 = 1032