ISEE Word Problems Question 243: Answer and Explanation
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Question: 243
7. The first six terms of an arithmetic sequence of numbers are shown.
–7, –4, –1, 2, 5, 8
Which expression gives the value of the xth term of the sequence?
- A. x – 8
- B. x – 6
- C. 3x – 10
- D. 3x + 7
Correct Answer: C
Explanation:
The answer is C
In an arithmetic sequence, the value of the xth term is given by d(x - 1) + S1, where d is the difference between terms and S1 is the value of the first term. Substitute the difference between the terms (3) and the value of the first term (-7): 3(x - 1) - 7. This is not an answer, however, so try distributing the 3: 3x - 3 - 7, which is 3x - 10.
As each term (x) yields a different value, select a term number and plug it into the answers to see which answer yields the correct value. To avoid dealing with negative numbers, pick the fourth term. In this case x = 4, and the expected value of the fourth term is 2. If you plug 4 into the answers, only choice (C) yields the expected value of 2.