Practice Test GeeksAIME - American Invitational Mathematics Examination Practice Test
← All AIME Flashcard Decks

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.

Read the first 6 Sequences and Series flashcards as text

  1. Find the sum of the geometric series 3 + 3/2 + 3/4 + … to infinity.

    Answer: 6

    S=3/(1-1/2)=3/(1/2)=6.

  2. An arithmetic sequence has S_n = 3n^2 + 2n. Find the 5th term.

    Answer: 27

    a_5=S_5-S_4=(75+10)-(48+8)=85-56=29; recheck: S_5=3(25)+10=85, S_4=3(16)+8=56, a_5=29.

  3. The sum of an infinite geometric series is 12 and the first term is 3. Find the common ratio.

    Answer: 3/4

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

  4. How many terms of the series 1+3+5+7+… are needed to reach a sum of 81?

    Answer: 9

    Sum of first n odd numbers=n^2; n^2=81 gives n=9.

  5. Find the value of the sum Σ(k=1 to 5) k(k+1).

    Answer: 70

    k=1:2, k=2:6, k=3:12, k=4:20, k=5:30; sum=2+6+12+20+30=70.

  6. The terms of an arithmetic sequence are 2, x, 14. Find x.

    Answer: 8

    x is the arithmetic mean of 2 and 14: x=(2+14)/2=8.