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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.

Read the first 7 NBT Mathematics: Sequences, Series and Patterns flashcards as text

  1. What is the sum of all integers from 1 to 100?

    Answer: 5050

    Sₙ = n(n+1)/2 = 100(101)/2 = 5050.

  2. A sequence has Tₙ = 5 × 2ⁿ⁻¹. Which statement is true?

    Answer: It is geometric with r = 2

    The formula Tₙ = arⁿ⁻¹ with a = 5 and r = 2 defines a geometric sequence.

  3. If ∑ₙ₌₁⁸ aₙ = 96 and each term is equal, what is each term?

    Answer: 12

    If all 8 terms are equal, each term = 96 ÷ 8 = 12.

  4. The 4th term of an arithmetic sequence is 25 and the 9th term is 50. What is the common difference?

    Answer: 5

    T₉ − T₄ = 5d = 25 → d = 5.

  5. A pattern of squares: 1st figure has 1 square, 2nd has 5, 3rd has 13, 4th has 25. What is the general term?

    Answer: Tₙ = 2n² − 2n + 1

    Tₙ = 2n²−2n+1 gives T₁=1, T₂=5, T₃=13, T₄=25, matching the pattern exactly.

  6. Which value of r makes the infinite geometric series ∑ arⁿ diverge?

    Answer: r = 1.2

    An infinite geometric series converges only when |r| 1 so it diverges.

  7. The first term of a sequence is 64 and each subsequent term is half the previous. What is the sum of the first 6 terms?

    Answer: 126

    S₆ = 64(1 − (1/2)⁶)/(1 − 1/2) = 64(63/64)/(1/2) = 63 × 2 = 126.