AMC12 Sequences & Series

Question 1

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

Accepted Answer

39

Answer

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

Question 2

What is the sum of the first 20 positive integers?

Accepted Answer

210

Answer

S_20=20*21/2=210.

Question 3

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

Accepted Answer

3

Answer

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

Question 4

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

Accepted Answer

2

Answer

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

Question 5

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

Accepted Answer

3

Answer

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

AMC12 - American Mathematics Competition 12 Practice Test