6.4: Arithmetic Sequences
Pg. 385 – 387: #2b, 3b, 5b, 6, 7ac, 10ac, 13, 15, 17, 23
Question 2
b) The first term is a = 2 and the differences increase by 1 for each successive pair of terms. The sequence is not arithmetic.
Question 3
b) The first three terms are –2, –6, –10.
Determine the general term.
tn  a  (n  1)d
 2  (n  1)(4)
 2  4n  4
 4n  2
The general term is tn = –4n + 2.
Question 5
b) The first three terms of the sequence are –2, –1, 0.
f(n)
n
Question 6
Let n represent the position of the term.
Substitute tn = –146, a = 9, and d = –5 into the general term for an arithmetic sequence.
tn  a  (n  1)d
146  9  (n  1)(5)
146  9  5n  5
5n  160
n  32
Term 32 is –146.
Question 7
a) Substitute tn = 200, a = 5, and d = 5 into the general term for an arithmetic sequence.
tn  a  (n  1)d
200  5  (n  1)(5)
200  5  5n  5
200  5n
n  40
The sequence contains 40 terms.
c) Substitute tn = –269, a = –5, and d = –3 into the general term for an arithmetic sequence.
tn  a  (n  1)d
269  5  (n  1)(3)
269  5  3n  3
3n  267
n  89
The sequence contains 89 terms.
Question 10
a) For t8:
33 = a + 7d

For t14:
57 = a + 13d

Subtract equation  from equation .
24  6d
d 4
Substitute d = 4 into equation .
33  a  7 d
33  a  7(4)
33  28  a
a5
Determine the general term.
tn  a  (n  1)d
 5  ( n  1)(4)
 5  4n  4
 4n  1
The general term is tn = 4n + 1.
c) For t5:
–20 = a + 4d

For t18:
–59 = a + 17d

Subtract equation  from equation .
39  13d
d  3
Substitute d = –3 into equation .
20  a  4d
20  a  4(3)
20  12  a
a  8
Determine the general term.
tn  a  (n  1)d
 8  ( n  1)(3)
 8  3n  3
 3n  5
The general term is tn = –3n – 5.
Question 13
a) The prizes form an arithmetic sequence with a = 10 000 and d = –500.
The tenth prize corresponds to t10.
tn  a  (n  1)d
 10 000  (10  1)(500)
 10 000  4500
 5500
The tenth winner receives $5500.
b) The smallest prize is $500. Determine the value of n that corresponds to this amount.
tn  a  (n  1)d
500  10 000  (n  1)(500)
500  10 000  500n  500
500n  10 000
n  20
There are 20 possible winners in total.
Question 15
For t2:
870 = a + d

For t7:
1110 = a + 6d

Subtract equation  from equation .
240  5d
d  48
Substitute d = 48 into equation .
870  a  48
a  822
There were 822 members the first week.
Question 17
The least number between –58 and 606 that is divisible by 8 is –56. The greatest number between –58 and 606 that is divisible
by 8 is 600. the largest is 600. Consider an arithmetic sequence with a = –56, d = 8 and tn = 600.
tn  a  (n  1)d
600  56  (n  1)(8)
600  56  8n  8
664  8n
n  83
There are 83 multiples of 8 between –58 and 606.
Question 23
In order for Sam to say a number, the difference between that number and 412 must be divisible by 6. By inspection,
412  58
 59 . The other choices fail this test. The correct choice is C.
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