Download MCR3UI 1. Use the recursion formula to write the first 5 terms of

MCR3UI
1.
Use the recursion formula to write the first 5 terms of each sequence.
a) 𝑡1 = 4; 𝑡𝑛 = 𝑡𝑛−1 + 3
b) 𝑡1 = −1; 𝑡𝑛 = 2𝑡𝑛−1
d)
2.
c)
𝑡1 = 6; 𝑡𝑛 = 𝑡𝑛−1 + 2𝑛
𝑡1 = 2; 𝑡𝑛 = 4𝑡𝑛−1 + 𝑛2
Use the recursion formula to write the first 5 terms of each sequence.
a) 𝑡1 = −2; 𝑡2 = 3; 𝑡𝑛 = 2𝑡𝑛−2 + 𝑡𝑛−1
b) 𝑡1 = 2; 𝑡2 = 1; 𝑡𝑛 = 𝑡𝑛−2 + 𝑡𝑛−1 − 2𝑛
c)
𝑡1 = −1; 𝑡2 = 2; 𝑡3 = 4; 𝑡𝑛 = 2𝑡𝑛−3 − 𝑡𝑛−2 + 3𝑡𝑛−1
3.
Use the recursion formula to write the first 6 terms of the sequence:
𝑓(1) = 1.5; 𝑓(2) = 2.5; 𝑓(𝑛) = 𝑓(𝑛 − 1) + 𝑓(𝑛 − 2)
4.
Write an explicit formula for the sequence determine by each recursion formula.
a)
𝑡1 = 1; 𝑡𝑛 = 𝑡𝑛−1 − 4
1
2
𝑡1 = 20; 𝑡𝑛 = − 𝑡𝑛−1
b)
5.
The number of seats in the rows of a theatre are represented by the recursion formula 𝑡1 = 20; 𝑡𝑛 = 𝑡𝑛−1 + 2.
a) Determine the number of seats in each of the first 8 rows.
b) Write and explicit formula to represent the number of seats in the 𝑛𝑡ℎ row.
6.
a)
b)
c)
Write the first 6 terms of the sequence determine by the recursion formula 𝑡1 = 1; 𝑡𝑛 = 𝑡𝑛−1 + 2𝑛 − 1.
What do all the numbers in the sequence have in common?
Write an explicit formula for the 𝑛𝑡ℎ term of the sequence.
7.
a)
Write the first 5 terms of a sequence determined by the recursion formula 𝑡1 = 𝑥 and 𝑡𝑛 = 𝑥 ×
b)
Write an explicit formula for the 𝑛𝑡ℎ term of the sequence.
Answers
1a) 4, 7, 10, 13
1b) -1, -2, -4, -8, -16
3) 1.5, 2.5 4, 6.5, 10.5 17
6a) 1, 4, 9, 16, 25, 36
1c) 6, 10, 16, 24, 34
4a) 𝑡𝑛 = −4𝑛 + 5
1d) -2, -4, -7, -12, -23
1 𝑛−1
4b) 𝑡𝑛 = 20 (− )
6b) They are all perfect squares
2
6c) 𝑡𝑛 = 𝑛
2
2a) -2, 3, -1, 5, 3,
2b) 2, 1 -3, -10, -23
5b) 𝑡𝑛 = 2𝑛 + 18
5a) 20, 22, 24, 26, 28, 30, 32, 34
7a) 𝑥,
𝑥2 𝑥3 𝑥4 𝑥5
2
,
4
,
8
,
16
𝑥 𝑛−1
7b) 𝑡𝑛 = 𝑥 ( )
2
𝑡𝑛−1
.
2
2c) -1, 2, 4, 8, 24