SHSAT Math Quiz: Predicting Later Terms
4 questions · exam conditions
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Predicting Later TermsQuestion 1 of 4

The first four terms of a sequence are 3, 7, 15, 31. If this pattern continues, which expression represents the nth term?

2n+1−12^{n+1} - 1
2n+n−12^n + n - 1
4n−14n - 1
2n+1+n−22^{n+1} + n - 2
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SHSAT Math Quiz

SHSAT Math Quiz: Predicting Later Terms

Practice Predicting Later Terms in SHSAT Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Predicting Later Terms, giving you a quick way to practice the rules, question types, and explanations that matter most for SHSAT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The first four terms of a sequence are 3, 7, 15, 31. If this pattern continues, which expression represents the nth term?

  1. 2n+1−12^{n+1} - 1 (correct answer)
  2. 2n+n−12^n + n - 1
  3. 4n−14n - 1
  4. 2n+1+n−22^{n+1} + n - 2
Explanation: Examine the differences: 7-3=4, 15-7=8, 31-15=16. The differences are powers of 2: 22,23,242^2, 2^3, 2^4. This suggests each term is related to powers of 2. Testing the pattern: 3 = 22−1=4−12^2 - 1 = 4 - 1, 7 = 23−1=8−12^3 - 1 = 8 - 1, 15 = 24−1=16−12^4 - 1 = 16 - 1, 31 = 25−1=32−12^5 - 1 = 32 - 1. So the nth term is 2n+1−12^{n+1} - 1. Choice B gives different values. Choice C is linear, not exponential. Choice D adds unnecessary complexity.

Question 2

The sequence 5,  9,  13,  17,  …5,\;9,\;13,\;17,\;\dots follows a consistent pattern. What is the 50th term of the sequence?

  1. 197197
  2. 201201 (correct answer)
  3. 205205
  4. 209209
Explanation: When you encounter a sequence like this, you're dealing with an arithmetic sequence—a pattern where the same number is added each time. Your first step is to identify the common difference by subtracting consecutive terms. Looking at the given sequence: 5,9,13,17,…5, 9, 13, 17, \dots The common difference is 9−5=49 - 5 = 4, and you can verify this: 13−9=413 - 9 = 4 and 17−13=417 - 13 = 4. So we're adding 4 each time. For any arithmetic sequence, the formula for the nth term is: an=a1+(n−1)da_n = a_1 + (n-1)d, where a1a_1 is the first term and dd is the common difference. Here, a1=5a_1 = 5 and d=4d = 4, so: a50=5+(50−1)×4=5+49×4=5+196=201a_{50} = 5 + (50-1) \times 4 = 5 + 49 \times 4 = 5 + 196 = 201 Looking at the wrong answers: Choice A (197197) comes from miscalculating 49×449 \times 4 as 192192 instead of 196196. Choice C (205205) results from using n=50n = 50 instead of (n−1)=49(n-1) = 49 in the formula, giving you 5+50×4=2055 + 50 \times 4 = 205. Choice D (209209) compounds both errors: using nn instead of (n−1)(n-1) and then adding an extra 4. The correct answer is B: 201201. Study tip: Always double-check your arithmetic sequence formula—it's (n−1)d(n-1)d, not ndnd, because you don't add the common difference to get to the first term. Practice identifying the pattern first, then apply the formula carefully.

Question 3

A piecewise sequence is defined as: f(n)={2n+1if n is oddn2−1if n is evenf(n) = \begin{cases} 2n + 1 & \text{if } n \text{ is odd} \\ n^2 - 1 & \text{if } n \text{ is even} \end{cases} . What is the value of f(15)+f(16)f(15) + f(16)?

  1. 286 (correct answer)
  2. 287
  3. 288
  4. 289
Explanation: Since 15 is odd: f(15)=2(15)+1=30+1=31f(15) = 2(15) + 1 = 30 + 1 = 31. Since 16 is even: f(16)=162−1=256−1=255f(16) = 16^2 - 1 = 256 - 1 = 255. Therefore: f(15)+f(16)=31+255=286f(15) + f(16) = 31 + 255 = 286. Choice B results from adding 1 extra. Choice C results from forgetting to subtract 1 from 16216^2. Choice D combines both errors.

Question 4

A Fibonacci-like sequence starts with a1=1a_1 = 1 and a2=3a_2 = 3, where each subsequent term equals the sum of the two preceding terms. If an=199a_n = 199, what is the value of an+2a_{n+2}?

  1. 521 (correct answer)
  2. 643
  3. 721
  4. 843
Explanation: First, generate the sequence: a1=1,a2=3,a3=4,a4=7,a5=11,a6=18,a7=29,a8=47,a9=76,a10=123,a11=199a_1 = 1, a_2 = 3, a_3 = 4, a_4 = 7, a_5 = 11, a_6 = 18, a_7 = 29, a_8 = 47, a_9 = 76, a_{10} = 123, a_{11} = 199. So n=11n = 11. We need a13a_{13}. a12=a10+a11=123+199=322a_{12} = a_{10} + a_{11} = 123 + 199 = 322. a13=a11+a12=199+322=521a_{13} = a_{11} + a_{12} = 199 + 322 = 521. Choice B assumes an incorrect sequence position. Choice C uses wrong arithmetic. Choice D doubles one of the terms incorrectly.