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NBT Mathematics: Sequences, Series and Patterns Flashcards

7 cards from real NBT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. The sum of the first n terms of a series is given by Sₙ = 3n² − n. What is T₄?

    Answer: 20

    T₄ = S₄ − S₃ = (3×16−4) − (3×9−3) = 44 − 24 = 20.

  2. A geometric sequence has T₂ = 6 and T₅ = 162. What is the first term?

    Answer: 2

    T₅/T₂ = r³ = 162/6 = 27 → r = 3; T₁ = T₂/r = 6/3 = 2.

  3. How many terms of the series 8 + 11 + 14 + … are needed for the sum to first exceed 100?

    Answer: 7

    Sₙ = n/2(16 + 3(n−1)) > 100. For n=7: S₇ = 7/2(37) = 129.5 > 100; S₆ = 3(32) = 96 < 100.

  4. Express 0.\overline{36} as a fraction in lowest terms.

    Answer: 4/11

    0.363636… = 36/99 = 4/11.

  5. The nth term of a sequence is Tₙ = n(n + 2). Which of the following is NOT a term of this sequence?

    Answer: 10

    Tₙ = n(n+2) gives 3, 8, 15, 24 for n=1,2,3,4. The value 10 is between T₂=8 and T₃=15 and cannot be produced.

  6. If the first term of a geometric sequence is 81 and the common ratio is 1/3, what is S∞?

    Answer: 121.5

    S∞ = 81/(1 − 1/3) = 81/(2/3) = 81 × 3/2 = 121.5.

  7. Determine the value of k if 2k, k + 3, and k − 1 are three consecutive terms of an arithmetic sequence.

    Answer: k = 1

    (k+2)² = k(k+8) → k²+4k+4 = k²+8k → 4k = 4 → k = 1. Verify: 1, 3, 9 has r=3. ✓