Find a general term for the given terms of each sequence. See Example 2.
23. , , , 24.
25. 26. , , ,
Solve each applied problem by writing the first few terms of a sequence. See Example 3.
27.Horacio Loschak borrows $1000 and agrees to pay $100 plus interest of 1% on the unpaid
balance each month. Find the payments for the first six months and the remaining debt at
the end of that period.
28.Leslie Maruri is offered a new modeling job with a salary of dollars per
year at the end of the nth year. Write a sequence showing her salary at the end of each of the
first 5 yr. If she continues in this way, what will her salary be at the end of the tenth year?
29.Suppose that an automobile loses of its value each year; that is, at the end of any given
year, the value is of the value at the beginning of that year. If a car costs $20,000 new,
what is its value at the end of 5 yr, to the nearest dollar?30.A certain car loses of its value each year. If this car cost $40,000 new, what is its value
at the end of 6 yr?
Write out each series and evaluate it. See Example 4.
33. 34.
35. 36.
37. 38.
Write each series with summation notation. See Example 5.
45.Explain the basic difference between a sequence and a series.
46.Concept Check Consider the following statement.WHAT WENT WRONG?
For the sequence defined by , find.Find the arithmetic mean for each collection of numbers. See Example 6.
47.8, 11, 14, 9, 7, 6, 8 48.10, 12, 8, 19, 23, 12
49.5, 9, 8, 2, 4, 7, 3, 2, 0 50.2, 1, 4, 8, 3, 7, 10, 8, 0
an= 2 n+ 4 a1/21 + 4 + 9 + 16 1 + 16 + 81 + 256
- 2 + 4 - 8 + 16 - 32 - 1 + 2 - 3 + 4 - 5 + 6
3 + 4 + 5 + 6 + 7 7 + 8 + 9 + 10 + 11
a6i= 2a^1 i+^321 i-^427i= 31 i- 321 i+ 22a5i= 1a^1 -^12 i#i
6i= 11 - 12 ia4i= 1a^1 i^3 +^323i= 11 i^2 + 22a6i= 1a^1 i+^925i= 11 i+ 321
24
51
520,000+ 2500 n4
5
,Á
3
4
2
3
1
2
2
5
,
3
6
,
4
7
,
5
8
,Á
2
5
,
2
25
,
2
125
,
2
625
,Á
1
81
,Á
1
27
1
9
1
3
- 8, -16, -24, -32,Á -10, -20, -30, -40,Á
4, 8, 12, 16,Á 7, 14, 21, 28,Á
an