Practice Test GeeksAIME - American Invitational Mathematics Examination Practice Test
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Sequences and Series Flashcards

6 cards from real AIME 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 and 6th terms of a geometric sequence are 8 and 64. Find the common ratio.

    Answer: 2

    a_6/a_3=r^3=64/8=8 so r=2.

  2. Find the number of terms in the arithmetic sequence 5, 9, 13, …, 101.

    Answer: 25

    101=5+(n-1)×4 gives n-1=24, so n=25.

  3. Find the sum 1+2+3+…+100.

    Answer: 5050

    S=n(n+1)/2=100×101/2=5050.

  4. If the first term of a geometric series is 1/2 and the sum to infinity is 2, find the common ratio.

    Answer: 3/4

    S=a/(1-r)=2 so 1/2/(1-r)=2, giving 1-r=1/4, r=3/4.

  5. In the Fibonacci sequence 1,1,2,3,5,8,13,…, what is the 9th term?

    Answer: 34

    Continuing: 1,1,2,3,5,8,13,21,34; the 9th term is 34.

  6. For the sequence a_n = n^2 - n, find a_7 - a_5.

    Answer: 22

    a_7=49-7=42, a_5=25-5=20; difference=22.