HSPT Question of the Day

1. 210
2. 225 (correct answer)
3. 240
4. 256

Explanation: When you see a sequence of numbers, your first step is to identify the pattern. Looking at this sequence: $1, 4, 9, 16, 25, 36, ...$ you should recognize these as perfect squares. Notice that $1 = 1^2$, $4 = 2^2$, $9 = 3^2$, $16 = 4^2$, $25 = 5^2$, and $36 = 6^2$. This means the $n$th term of the sequence is simply $n^2$. To find the 15th term, you calculate $15^2 = 15 \times 15 = 225$. Let's examine why the other answers are wrong. Choice A (210) might tempt you if you mistakenly think this is an arithmetic sequence and try to find a common difference, but there's no consistent difference between consecutive terms. Choice C (240) could result from calculation errors when squaring 15, perhaps confusing it with $15 \times 16$. Choice D (256) is actually $16^2$, so you'd get this if you miscounted and thought you needed the 16th term instead of the 15th. The key strategy for sequence problems is pattern recognition. Perfect squares appear frequently on standardized tests, so memorizing the first 15-20 perfect squares will save you time. When you see $1, 4, 9, 16...$ immediately think "perfect squares" rather than trying to find differences between terms. This recognition allows you to jump straight to the formula $n^2$ and solve quickly.