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.

Read the first 6 Sequences & Series flashcards as text

  1. What is the 10th term of the arithmetic sequence 3, 7, 11, ...?

    Answer: 39

    a_10=3+(10-1)*4=3+36=39.

  2. What is the sum of the first 20 positive integers?

    Answer: 210

    S_20=20*21/2=210.

  3. What is the common ratio of the geometric sequence 2, 6, 18, ...?

    Answer: 3

    Each term is multiplied by 6/2=3 to get the next, so the common ratio is 3.

  4. What is the sum to infinity of 1 + 1/2 + 1/4 + ...?

    Answer: 2

    S=a/(1-r)=1/(1-1/2)=2.

  5. The 5th term of an arithmetic sequence is 17 and the 10th term is 32. What is the common difference?

    Answer: 3

    d=(32-17)/(10-5)=15/5=3.

  6. What is the sum of the infinite geometric series 3 + 1 + 1/3 + ...?

    Answer: 9/2

    S=3/(1-1/3)=3/(2/3)=9/2.