ISEE Upper Level Quantitative Reasoning Question of the Day

1. 77 (correct answer)
2. 79
3. 81
4. 83

Explanation: When you encounter arithmetic sequence problems, you're working with patterns where each term increases by the same constant difference. The key is finding that common difference and using the arithmetic sequence formula. In an arithmetic sequence, any term can be found using $a_n = a_1 + (n-1)d$, where $a_1$ is the first term and $d$ is the common difference. Since you know the 3rd term is 17 and the 8th term is 42, you can set up equations: $a_3 = a_1 + 2d = 17$ and $a_8 = a_1 + 7d = 42$. To find the common difference, subtract the first equation from the second: $(a_1 + 7d) - (a_1 + 2d) = 42 - 17$, which gives you $5d = 25$, so $d = 5$. Now find the first term by substituting back: $a_1 + 2(5) = 17$, so $a_1 = 7$. For the 15th term: $a_{15} = 7 + (15-1)(5) = 7 + 70 = 77$. Looking at the wrong answers: B) 79 results from miscalculating the common difference as 6 instead of 5. C) 81 comes from incorrectly using $d = 5$ but making an arithmetic error in the final calculation. D) 83 typically results from finding the wrong first term, perhaps using $a_1 = 9$ instead of 7. Remember this pattern: when given two terms in an arithmetic sequence, always subtract to find the common difference first. The difference between the terms divided by the difference between their positions gives you $d$.