MCR 3U Functions
Grade 11
SEQUENCES AND
SERIES TEST 1
K/U
APP
𝟏𝟕
TIPS
COM
𝟏𝟑
𝟐𝟎
𝟖
Answers must be clear and complete for full marks. Two
marks will be given for overall form.
Knowledge and Understanding
1. State the general term for sequence – 108, 36, – 12, 4, …
𝟐. State a recursion formula for the sequence 9, 16, 23, 30, …
[1]
[1]
3. Write the first 5 terms of the sequence defined by the following
recursion formula: [3]
𝑡1 = 3, 𝑡2 = −1,
𝑡𝑛 = (𝑡𝑛 − 1 )2 + 2𝑡𝑛 − 2 , 𝑛 > 2.
4. Determine the sum of the first 30 terms of the series 1 + 10 +
19 + 28 + … . [2]
5. Determine the sum of the series − 7 − 14 − 28 − 56 − … − 7168.
[4]
6. Which row in Pascal’s triangle has a sum of 512? [2]
7. Use Pascal’s triangle to expand the following binomials.
a) (4𝑥 − 𝑦 2 )5
[3]
1 4
b) (√2𝑥 + )
𝑥
[4]
Application
8. How many terms in the sequence
000? [3]
1 1
, , 1, 3, … are less than 1 000
9 3
9. The arithmetic sequence 1 + 4 + 7 + 10 + ⋯ + 𝑡𝑛 has the sum of
1001. How many terms does the series have? [4]
10. A student council is going to sell tickets for a candy-give-away.
Each person who buys a $3 ticket
will have his/her name put into lottery. All the names will be drawn
and the first person will receive
1 candy, the second person – 2 candies, the third person – 4
candies, the fourth person – 8 candies,
and so on. Student council predicts that they will sell 25 tickets.
a) How many candies will the 25𝑡ℎ person receive? [4]
b) How many candies will the student council need to buy
altogether for 25 tickets? [2]
11. The six term of a geometric sequence is 10 and the tenth term is
160.
a) Find all possible values for the first term and the common ratio.
[4]
b) Use your values in a) to determine all possible values of 𝑡13 in
the sequence. [2]
Problem Solving
12. The first three terms of an expanded binomial are 128 𝑥 7 −
1344 𝑥 6 𝑦 2 + 6048 𝑥 5 𝑦 4 − … .
Write the binomial in the form (𝑎 + 𝑏)𝑛 .
[3]
11. Amara earns a monthly paycheck of $3100. In order to save for a car
she decides to deposit a portion
of each monthly paycheck into a savings account. The first month
she deposits 10% of her paycheck,
the second month she deposits 11% of her paycheck, the third
month she deposits 12%, the fourth
month she deposits 13% and so on for a full year. How much will
she have in her savings account
after 12 months? [4]
12. The second term of an arithmetic series is 10 and the sum of the first
18 terms is 1125. Find the value
of the 100𝑡ℎ term in the series. [6]
Communication
13. Is it possible to have a sequence that is both arithmetic and
geometric? If so, give an example. If not,
clearly explain why it is not possible. [2]
14. Determine whether each sequence is arithmetic, geometric or
neither. Explain using proper
mathematical terminology.
a)
2 1 3
, , ,
9
3 2 8 32
,…
b) 1, 2, 4, 7, ... [2]
[2]