HSPT Quantitative Question of the Day

1. $121$ (correct answer)
2. $117$
3. $109$
4. $131$

Explanation: When you encounter a sequence problem, look for patterns in how terms relate to each other. This could involve differences between consecutive terms, ratios, or more complex recursive relationships. Let's examine the differences between consecutive terms: $4-1=3$, $13-4=9$, $40-13=27$. Notice that $3=3^1$, $9=3^2$, and $27=3^3$. The differences follow powers of 3! If this pattern continues, the next difference should be $3^4=81$. So the missing term would be $40+81=121$. Let's verify by checking if this works for the remaining terms: $364-121=243=3^5$ and $1093-364=729=3^6$. Perfect! The complete sequence has differences of $3^1, 3^2, 3^3, 3^4, 3^5, 3^6$, confirming our pattern. Looking at the wrong answers: Choice B ($117$) would create a difference of $77$, which doesn't fit the powers of 3 pattern. Choice C ($109$) gives a difference of $69$, also breaking the pattern. Choice D ($131$) produces a difference of $91$, which similarly doesn't align with $3^4=81$. The correct answer is A) $121$. Strategy tip: For sequence problems on the HSPT, always look for patterns in differences between terms first. If the first differences don't show an obvious pattern, check if they follow powers, factorials, or geometric progressions. Write out several differences to spot the underlying mathematical relationship before trying to guess the missing term.