COMC Functions and Sequences 2

Question 1

The 3rd term of a geometric sequence is 12 and the 6th term is 96. What is the common ratio?

Accepted Answer

2

Answer

t₆ / t₃ = r³ = 96/12 = 8, so r = 2.

Question 2

The sum of the first n terms of a sequence is Sₙ = 3n² + 2n. What is the 5th term?

Accepted Answer

29

Answer

a₅ = S₅ − S₄ = (75+10) − (48+8) = 85 − 56 = 29.

Question 3

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

Accepted Answer

2/3

Answer

The series has first term a = 1 and ratio r = −1/2, so S = 1/(1 − (−1/2)) = 2/3.

Question 4

A sequence satisfies aₙ₊₁ = 2aₙ − 1 with a₁ = 3. What is a₅?

Accepted Answer

33

Answer

a₂=5, a₃=9, a₄=17, a₅=33.

Question 5

The sum of the first n odd positive integers 1 + 3 + 5 + · · · + (2n−1) equals which expression?

Accepted Answer

n²

Answer

This is the classical identity: the sum of the first n odd integers equals n².

COMC - Canadian Open Mathematics Challenge Practice Test