AIME Sequences and Series

Question 1

Find the 10th term of the arithmetic sequence 3, 7, 11, 15, …

Accepted Answer

39

Answer

a_n=3+(n-1)×4; a_10=3+36=39.

Question 2

What is the sum of the first 20 terms of the arithmetic sequence 2, 5, 8, 11, …?

Accepted Answer

610

Answer

S_20=20/2×(2·2+19·3)=10×(4+57)=10×61=610.

Question 3

Find the common ratio of the geometric sequence 3, 6, 12, 24, …

Accepted Answer

2

Answer

Each term is doubled: ratio = 6/3 = 2.

Question 4

Find the 6th term of the geometric sequence 2, 6, 18, …

Accepted Answer

486

Answer

a_6=2×3^5=2×243=486.

Question 5

What is the sum of the infinite geometric series 4 + 2 + 1 + 1/2 + …?

Accepted Answer

8

Answer

S=a/(1-r)=4/(1-1/2)=4/(1/2)=8.

AIME - American Invitational Mathematics Examination Practice Test