Chapter 12 Sequences; Induction; the Binomial Theorem

Chapter 12: Sequences; Induction; the Binomial Theorem
c. Scroll through the table:
(d) Scroll through the table:
At the beginning of the 33rd month, or after
32 payments have been made, the balance is
below $4,000. The balance is $3982.8.
d. Scroll through the table:
At the beginning of the 192nd month, or
after 191 payments have been made, the
balance is below $100,000. The
balance is about $99,288.
(e) Scroll through the table:
The loan will be paid off after 289
months. They will make 288 payments
of $1332.34 plus a last payment of
$1142.80 plus interest. The total
amount paid is:
⎛ 0.0675 ⎞
288(1332.34) + 1142.80⎜1+
⎟
⎝ 12 ⎠
≈ $384,863.15
(f) The total interest expense is the
difference of the total of the payments
and the original loan:
384,863.15 − 190,000 = $19,863.15 .
69. a. b1 = 5,000, bn
= 1.015bn
− 1−
100
b2 = 1.015b( 2−1)
− 100 = 1.015b1−100
= 1.015 5000 − 100 = $4975
( )
b. Enter the recursive formula in Y= and draw
the graph:
The balance will be paid off at the end of 94
months or 7years and 10 months.
Total payments =
100(93) + 11.01 1.015 = $9,311.18
( )
e. The total interest expense is the difference
between the total of the payments and the
original balance:
100(93) + 11.18 − 5,000 = $4,311.18
70. This is a geometric sequence with
a1 = 20,000, r = 1.04, n = 5 . Find the fifth term
of the sequence:
5−1 4
a 5 = 20,000(1.04) = 20,000(1.04) = 23,397.17
Her salary in the fifth year will be $23,397.17.
Chapter 12 Test
1.
2
n −1
an
=
n + 8
2 2
1 −1 0 2 −1 3
a1 = = = 0, a2
= = ,
1+ 8 9 2+
8 10
2 2
3 −1 8 4 −1 15 5
a3 = = , a4
= = = ,
3+ 8 11 4+
8 12 4
2
5 −1 24
a5
= =
5+
8 13
The first five terms of the sequence are 0, 3
10 ,
8
11 , 5 24
, and
4 13 .
1280
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