AIME Sequences and Series 2

Question 1

The 3rd and 6th terms of a geometric sequence are 8 and 64. Find the common ratio.

Accepted Answer

2

Answer

4

Answer

3

Answer

8

Question 2

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

Accepted Answer

25

Answer

20

Answer

30

Answer

24

Question 3

Find the sum 1+2+3+…+100.

Accepted Answer

5050

Answer

5000

Answer

4950

Answer

5100

Question 4

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

Accepted Answer

3/4

Answer

1/2

Answer

1/4

Answer

1/3

Question 5

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

Accepted Answer

34

Answer

21

Answer

55

Answer

13

Question 6

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

Accepted Answer

22

Answer

20

Answer

24

Answer

18