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Functions and Sequences Flashcards

7 cards from real COMC 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 3rd term of a geometric sequence is 12 and the 6th term is 96. What is the common ratio?

    Answer: 2

    t₆ / t₃ = r³ = 96/12 = 8, so r = 2.

  2. The sum of the first n terms of a sequence is Sₙ = 3n² + 2n. What is the 5th term?

    Answer: 29

    a₅ = S₅ − S₄ = (75+10) − (48+8) = 85 − 56 = 29.

  3. What is the sum of the infinite geometric series 1 − 1/2 + 1/4 − 1/8 + · · ·?

    Answer: 2/3

    The series has first term a = 1 and ratio r = −1/2, so S = 1/(1 − (−1/2)) = 2/3.

  4. A sequence satisfies aₙ₊₁ = 2aₙ − 1 with a₁ = 3. What is a₅?

    Answer: 33

    a₂=5, a₃=9, a₄=17, a₅=33.

  5. The sum of the first n odd positive integers 1 + 3 + 5 + · · · + (2n−1) equals which expression?

    Answer: n²

    This is the classical identity: the sum of the first n odd integers equals n².

  6. In an arithmetic sequence, the sum of the 3rd and 7th terms is 26, and the sum of the 4th and 8th terms is 30. What is the common difference?

    Answer: 2

    (a₄+a₈) − (a₃+a₇) = 2d = 30 − 26 = 4, so d = 2.

  7. The Fibonacci sequence is F₁=1, F₂=1, Fₙ=Fₙ₋₁+Fₙ₋₂ for n ≥ 3. What is F₁₀?

    Answer: 55

    The sequence begins 1,1,2,3,5,8,13,21,34,55, so F₁₀ = 55.