COMC Functions and Sequences 3

Question 1

A sequence satisfies a₁ = 1 and aₙ₊₁ = aₙ + n² for n ≥ 1. What is a₅?

Accepted Answer

31

Answer

25

Answer

28

Answer

36

Question 2

If f(n) = n(n+1)/2 (the nth triangular number), what is f(10) − f(7)?

Accepted Answer

27

Answer

21

Answer

30

Answer

34

Question 3

A sequence satisfies a₁ = 2, a₂ = 4, and aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. What is a₆?

Accepted Answer

26

Answer

18

Answer

22

Answer

30

Question 4

An infinite geometric series with first term a has sum 24. If a = 8, what is the common ratio r?

Accepted Answer

2/3

Answer

1/4

Answer

1/3

Answer

1/2

Question 5

A function on positive integers satisfies f(1) = 2 and f(n) = f(n−1) + 3 for n ≥ 2. Which closed form equals f(n)?

Accepted Answer

3n − 1

Answer

2n + 1

Answer

3n + 1

Answer

2n + 3

Question 6

If f(x) = x² + 1 and a sequence is defined by a₁ = 0, aₙ₊₁ = f(aₙ), what is a₃?

Accepted Answer

2

Answer

1

Answer

4

Answer

5

Question 7

A sequence satisfies a₁ = 2 and aₙ₊₁ = aₙ / (1 + aₙ). What is a₄?

Accepted Answer

2/7

Answer

1/4

Answer

1/3

Answer

2/9