Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Sequences & Series Flashcards

6 cards from real AMC12 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. If a_n = 2n-1, what is the sum of the first 10 terms?

    Answer: 100

    The first 10 odd numbers sum to 10^2=100.

  2. What is the sum from k=1 to 100 of (1/k - 1/(k+1))?

    Answer: 100/101

    This telescoping series sums to 1-1/101=100/101.

  3. In a geometric sequence the 3rd term is 18 and the 6th term is 486. What is the common ratio?

    Answer: 3

    r^3=486/18=27, so r=3.

  4. What is the sum of the arithmetic series 5 + 8 + 11 + ... + 50?

    Answer: 440

    There are (50-5)/3+1=16 terms; sum=16*(5+50)/2=8*55=440.

  5. What is the sum from k=1 to 10 of (2k-5)?

    Answer: 60

    Sum=2*sum(k)-5*10=2*55-50=110-50=60.

  6. An infinite geometric series has sum 12 and first term 3. What is the common ratio?

    Answer: 3/4

    3/(1-r)=12 gives 1-r=1/4, so r=3/4.