AMC 12 AMC 12 Sequences, Series & Limits

Question 1

What is the sum of the arithmetic series 1 + 2 + 3 + … + 100?

Accepted Answer

5050

Answer

100

Answer

1000

Answer

10100

Question 2

What is the common ratio of the geometric sequence 3, 6, 12, 24, …?

Accepted Answer

2

Answer

3

Answer

6

Answer

1/2

Question 3

What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + 1/8 + …?

Accepted Answer

2

Answer

1

Answer

3

Answer

∞

Question 4

In an arithmetic sequence with a₁ = 5 and common difference d = 3, what is a₁₀?

Accepted Answer

32

Answer

30

Answer

35

Answer

27

Question 5

What is the nth term of the geometric sequence 2, 6, 18, 54, …?

Accepted Answer

2·3^(n−1)

Answer

2·3^n

Answer

3·2^(n−1)

Answer

6^(n−1)

Question 6

What is the sum of the first 5 terms of a geometric series with a₁ = 4 and r = 2?

Accepted Answer

124

Answer

60

Answer

96

Answer

32