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Back to Lesson 8-3
Name
Lesson Master
Questions on SPUR Objectives
PROPERTIES Objective E
In 1–6, evaluate the arithmetic series.
a1 = – 2
an = an-1 + 7, for all integers n ≥ 2
_
1
4. 2.75, 2.875, 2.916 , 2.9375, …, 3 - _
,…
4n
(2)
5. tn = – 2 + _1 (n - 1)
( )
n-1
3n2 - 2n
8 –_
40 – _
7. – _17 , – _
, 21 , – _
, 13 , , – _
,
2
13
{
37
2n + 5
11
z1 = 4
zn =
( – _32 )z
n-1
, for all integers n > 1
In 9–12, let lim an = 3, lim bn = 6, and lim cn = 5. Find the limit.
n→∞
–3
20
n→∞
9. n→∞
lim (an - bn)
11. n→∞
lim (4cn)
n→∞
10. n→∞
lim (bn · cn)
( )
a nb n
12. n→∞
lim _
c
n
6
1.
374
Functions,
9. The roof of a shed is supported by 15 evenly spaced joists,
as shown at the right. One side of the roof has a length of
9 ft and makes a 36º angle with the horizontal.
18
__
5
a. Use Σ-notation to write the series representing
the total length of joists for one side of the roof
8
for one end of the shed.
∑( _13 )
joist
36º
n=1
b. Find the total length of the joists used for
both ends of the shed.
about 42.32 ft
Functions, Statistics, and Trigonometry
Lesson Master
Questions on SPUR Objectives
See Student Edition pages 555–557 for objectives.
375
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8-6
Lesson Master
n-1
≈ 1.498
In 1 and 2, to buy a motorboat, Mr. Spender borrows $13,000 at 7.75%
interest to be paid back in 42 monthly installments.
1. Identify each.
2. the sum of the first five terms of the sequence g where
g1 = 70
gn = –4gn-1, for all integers n > 1
11
∑ 4( – _35 )
i-1
i=1
2
4. the geometric series 18 + 6 + 2 + + _
81
10
∑(x )
5 n-1
n=1
6. the sum of the first fi fteen terms of the geometric
sequence with first term –4 and constant ratio _1
2
100
( )
7. Find ∑ _12
n=30
2( ( _12 ) - ( _12 )
29
n-1
.
14,350
a. the term of the loan
24,502,636
_______
9,765,625 ≈ 2.509
2186
____
81 ≈ 26.988
1-x50
____
1-x5
–32767
1
_____
____
4096 = –8 + 4096
100
) ≈ 3.725 · 10
–9
USES Objective H
8. On her birthday every year, starting at the age of 22 until retirement at
the age of 67, Beth plans to deposit $1800 into an Individual Retirement
Account (IRA). Suppose the IRA will earn 3.8% annual interest.
45
a. Using Σ-notation, write the series representing
the amount Beth will have in the account
t=1
when she retires.
∑1800(1.038)
b. Evaluate the series in Part a.
c. How much of the amount in Part b is interest?
9. A ball bounces two thirds of the height from which it falls.
What is the total distance traversed by a ball dropped
15 feet above the ground when it hits the ground
for the ninth time?
Functions,
Questions on SPUR Objectives
See Student Edition pages 555–557 for objectives.
USES Objective I
364
___
243
n=1
A20
t
9f
9n
∑__
8 sin(36º)
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6
376
i=1
25,200 lbs
30
SKILLS Objective C
5.
n=1
USES Objective G
y=3
3
In 1–6, evaluate.
3.
200
Name
8-5
{
4. the sum of the first
fi fty positive integers
8. To build up strength, Arnold started an exercise program in which
he did 10 repetitions of bicep curls with each arm three times each
week. He began lifting 10 lb weights, so the first week he lifted a total
of 10 · 2 · 3 · 10 = 600 lb. He added one additional lb to the weights
each week until he reached a total of 30 lb. What is the total amount
of weight Arnold lifted during this 21-week period?
Name
1.
1
4
500
Statistics, and Trigonometry
FST_TR-C08_LMA_Final.indd Page 376 5/25/10 9:18:07 AM s-0013
i=1
1275
–36,800
6. ∑ (17 - 2i)
10
7. The sum of the smallest k positive multiples of 5 is 275. Find k.
–
k=1
13. Use a graphing utility to graph an = n n + 2 for all integers n.
lim (x x + 2).
b. Find x→∞
∑ (2i + 3)
7
_1
_1
2.
n=1
REPRESENTATIONS Objective J
a. Give an equation for the horizontal
1
_
asymptote of the graph of y = x x + 2 .
45
5
∑ (3n - 5)
Functions,
c. the monthly interest rate
42 months
$13,000
≈ 0.6458%
2. a. How much would the bank have made on the principal if it
had not lent the borrower the $13,000 and instead invested
it at the same monthly compound interest rate?
b. How much will Mr. Spender’s monthly payment be?
3. Mrs. Charget took her family out to eat. She paid m dollars
for the meal with a charge card that requires 36 monthly
payments at 15% interest. If Mrs. Charget pays only the
minimum amount due, how much interest will she pay for her
family’s supper?
In 4 and 5, Mort Gage borrows $300,000 to purchase a house.
The loan is for a 30-year term at 6.4% interest.
4. What is Mr. Gage’s monthly payment?
t-1
≈ $206,360.41
≈ $123,560.41
about 72.659 ft
Statistics, and Trigonometry
b. the principal of the loan
5. If Mr. Gage makes an additional $100 payment each month,
how many months would it take him to repay the loan?
$17,035.74
$354.39
≈ 0.248m dollars
$1876.51
152 months, or 12
years and 8 months
In 6 and 7, Mr. Otto wishes to borrow $23,000 to buy a new car.
His bank offers two loans, Loan A is for 36 months at 3.4% and
Loan B is for 48 months at 3.9%.
6. How much smaller would Mr. Otto’s monthly payment be
for Loan B?
7. How much more total interest would Mr. Otto pay for Loan B?
about $154.64
about $652.43
Functions, Statistics, and Trigonometry
Copyright © Wright Group/McGraw-Hill
8.
23
33
3. ∑ ( 5 - _k) –42
2,880,750
5. ∑ 23n
convergent; 0
convergent; 2.3
divergent
convergent; 3
divergent
convergent; 0
convergent; – _32
divergent
2. kn = 2.3 for all integers n ≥ 2
6. gn = – 2 _12
Questions on SPUR Objectives
See Student Edition pages 555–557 for objectives.
SKILLS Objective C
n
5
2
0-0X
8-4 Lesson Master
See Student Edition pages 555–557 for objectives.
In 1–8, decide whether the sequence described is convergent or divergent.
If it is convergent, give the limit.
1. –6, –3, –2, – _3 , – _6 , –1, …, – _6 , …
{
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Name
8-3
3.
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377
Statistics, and Trigonometry
P DF P ass