Name:
Date:
MCR 3U1 – Unit 7 Test: Discrete Functions
K/U
/10
App
/10
Th
/5
Comm
PART A: KNOWLEDGE – Multiple Choice (5 Marks)
1. Determine the common difference for the sequence: 13, 17, 21, 25, 29, ...
a) 4
b) 5
c) -3
d) -4
2. Given that
t n  8  2n , the value of t 4
is
a) -8
c) 16
3. Given that
b) 0
d) -16
t n  2(3 n ) , the value of t 3
a) -162
c) -24
is
b) 162
d) -54
4. Given the series 6 +18 + 54 + …., find the value of S 7 .
a) 13116
c) 378
b) 4374
d) 6558
5. A formula used to calculate a term in a sequence from one or more previous terms is
called a(n)
a) arithmetic sequence
b) geometric sequence
c) explicit formula
d) recursion formula
Part B: KNOWLEDGE Short Answer (5 Marks)
Put your answer in the space provided. There is no need to show your work.
(1 mark each)
6. The explicit formula for the sequence 2, 8, 32, … is
_____________
7. A particular arithmetic sequence is defined by
The explicit formula would be
_____________
8. The number of terms in the sequence 80, 71, 62, 53, …, –280 is
_____________
9. The number of terms in the sequence 4, 12, 36, . . . , 2916 is
_____________
10. Given that a = 3, t n  147 and n = 19, find S n for the arithmetic
series.
_____________
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APPLICATION (10 Marks)
11. Write the explicit formula for the arithmetic sequence where t 7  121 and t15  193 .
(5 marks)
12.
Expand the binomial 2 x  3 using Pascal’s Triangle. (5 marks)
4
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THINKING – Choose ONE of the following questions!!!!!! (5 Marks)
13. a) The side lengths in a quadrilateral form an arithmetic sequence. The perimeter is
38 cm and the shortest side measures 5 cm. What are the lengths of the other
sides?
13. b) A farmer has to plant seeds in a triangular field. He knows that the middle
row, row 26, needs 4025 seeds, and that the last row needs 7525 seeds.
If the number of seeds planted in each row follows an arithmetic series,
how many total seeds does he need?
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COMMUNICATION (5 Marks)
14. You are given two sequences t1n = 4 + (n –1)7 and t2n = 4(2)n –1. Without
calculating, which term is bigger t1534 or t2534? Why? (3 marks)
15. Describe the difference between an arithmetic and geometric sequence.
(2 Marks)
BONUS (4 Marks)
Determine S 13 for x  x 7  7 x  7 x 7  ...
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