Math 1 Quiz: Modeling With Arithmetic Sequences
7 questions · exam conditions
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Modeling With Arithmetic SequencesQuestion 1 of 7

A pyramid is built using identical cubic blocks. The top layer has 1 block, the second layer has 4 blocks, the third layer has 7 blocks, and each subsequent layer has 3 more blocks than the layer above it. How many blocks are in the bottom layer if the pyramid has 8 layers total?

19 blocks
22 blocks
25 blocks
28 blocks
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Math 1 Quiz

Math 1 Quiz: Modeling With Arithmetic Sequences

Practice Modeling With Arithmetic Sequences in Math 1 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 Modeling With Arithmetic Sequences, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 1.

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

A pyramid is built using identical cubic blocks. The top layer has 1 block, the second layer has 4 blocks, the third layer has 7 blocks, and each subsequent layer has 3 more blocks than the layer above it. How many blocks are in the bottom layer if the pyramid has 8 layers total?

  1. 19 blocks
  2. 22 blocks (correct answer)
  3. 25 blocks
  4. 28 blocks
Explanation: The blocks per layer form an arithmetic sequence: 1, 4, 7, 10, 13, 16, 19, 22 for layers 1 through 8 (top to bottom). With first term a₁ = 1 and common difference d = 3, the 8th term is a₈ = 1 + (8-1)(3) = 1 + 21 = 22 blocks. The other choices represent common errors: 19 is the 7th layer, 25 would be if d = 4 instead of 3, and 28 would be if we miscounted the layers.

Question 2

A fitness program requires participants to do push-ups daily. Week 1 requires 20 push-ups per day, and each subsequent week increases by 8 push-ups per day. If a participant completes exactly 10 weeks of the program, what is the average number of push-ups per day over the entire program?

  1. 52 push-ups per day
  2. 56 push-ups per day (correct answer)
  3. 60 push-ups per day
  4. 64 push-ups per day
Explanation: The daily push-ups per week form an arithmetic sequence: 20, 28, 36, 44, 52, 60, 68, 76, 84, 92. The average of an arithmetic sequence equals the average of the first and last terms: (20 + 92)/2 = 112/2 = 56 push-ups per day. Alternatively, we can verify using the sum formula: S₁₀ = 10/2[2(20) + 9(8)] = 5[40 + 72] = 5(112) = 560 total push-ups per day across 10 weeks, so the average is 560/10 = 56 push-ups per day.

Question 3

A company's quarterly profits follow an arithmetic sequence. In the first quarter, they earned $45,000. By the fourth quarter of the same year, their profit had increased to $63,000. If this trend continues, what will be their total profit for the first two years (8 quarters)?

  1. $528,000 (correct answer)
  2. $552,000
  3. $576,000
  4. $504,000
Explanation: We have a₁ = 45,000 and a₄ = 63,000. Since a₄ = a₁ + 3d, we get 63,000 = 45,000 + 3d, so 3d = 18,000, giving d = 6,000. For 8 quarters: S₈ = 8/2[2(45,000) + (8-1)(6,000)] = 4[90,000 + 42,000] = 4(132,000) = $528,000. Choice B incorrectly uses d = 6,500. Choice C uses d = 7,000. Choice D uses only 7 quarters instead of 8.

Question 4

A theater has 24 seats in the first row, 28 seats in the second row, 32 seats in the third row, and so on. If the theater has 15 rows total and tickets cost $12 per seat, what is the total revenue when the theater is completely sold out?

  1. $7,080
  2. $8,400
  3. $7,560 (correct answer)
  4. $8,040
Explanation: First find the total number of seats using the arithmetic sequence formula. We have a₁ = 24, d = 4, n = 15. The sum is S₁₅ = 15/2[2(24) + (15-1)(4)] = 15/2[48 + 56] = 15/2(104) = 15(52) = 780 seats. Total revenue = 780 × $12 = $7,560. Choice A incorrectly uses 14 rows instead of 15. Choice B uses the wrong common difference of 6 instead of 4. Choice D results from arithmetic errors in the summation formula.

Question 5

A company implements a new employee bonus structure where each employee receives an initial bonus of $200 in January, and then receives an additional $75 each subsequent month. If an employee stays with the company for exactly 18 months under this plan, what is the total amount of bonuses they will receive?

  1. $1,475
  2. $1,550
  3. $2,825 (correct answer)
  4. $2,900
Explanation: This is an arithmetic sequence with first term a₁ = 200, common difference d = 75, and n = 18 terms. The sum formula is S_n = n/2[2a₁ + (n-1)d]. So S₁₈ = 18/2[2(200) + (18-1)(75)] = 9[400 + 17(75)] = 9[400 + 1275] = 9(1675) = $2,825. Choice A uses only 17 terms instead of 18. Choice B incorrectly adds 75 to choice A. Choice D incorrectly uses n = 18 instead of n-1 = 17 in the formula.

Question 6

A savings plan deposits $150 in the first month, $175 in the second month, $200 in the third month, and continues this pattern. After how many months will the account first contain more than $4,000 total?

  1. 12 months
  2. 13 months
  3. 14 months (correct answer)
  4. 15 months
Explanation: This is an arithmetic sequence with a₁ = 150, d = 25. We need the smallest n where S_n > 4000. Using S_n = n/2[2(150) + (n-1)(25)] = n/2[300 + 25n - 25] = n/2[275 + 25n]. Setting this > 4000: n(275 + 25n)/2 > 4000, so n(275 + 25n) > 8000, giving 275n + 25n² > 8000, or 25n² + 275n - 8000 > 0, or n² + 11n - 320 > 0. Using the quadratic formula: n = (-11 + √(121 + 1280))/2 = (-11 + √1401)/2 ≈ (-11 + 37.43)/2 ≈ 13.22. Since we need the first month where this exceeds $4000, we need n = 14. Choice A results from rounding errors. Choice B uses ≥ instead of >. Choice D adds an extra month unnecessarily.

Question 7

A medication dosage schedule starts with 400mg on day 1, then decreases by 25mg each day. On which day will the patient take their last dose before the medication is completely discontinued?

  1. Day 15
  2. Day 16 (correct answer)
  3. Day 17
  4. Day 18
Explanation: This is an arithmetic sequence with a₁ = 400 and d = -25. The general term is aₙ = 400 + (n-1)(-25) = 400 - 25(n-1) = 425 - 25n. The medication is discontinued when the dose would be 0 or negative. Setting 425 - 25n ≤ 0: 425 ≤ 25n, so n ≥ 17. On day 16: a₁₆ = 425 - 25(16) = 425 - 400 = 25mg. On day 17: a₁₇ = 425 - 25(17) = 425 - 425 = 0mg. So day 16 is the last day with a positive dose.