45.A seating section in a theater-in-the-round has 20 seats in the first row, 22 in the second
row, 24 in the third row, and so on for 25 rows. How many seats are there in the last row?
How many seats are there in the section?
46.Constantin Arne has started on a fitness program. He plans to jog 10 min per day for the
first week and then add 10 min per day each week until he is jogging an hour each day. In
which week will this occur? What is the total number of minutes he will run during the
first four weeks?
47.A child builds with blocks, placing 35 blocks in the first row, 31 in the second row, 27 in
the third row, and so on. Continuing this pattern, can she end with a row containing ex-
actly 1 block? If not, how many blocks will the last row contain? How many rows can she
build this way?
48.A stack of firewood has 28 pieces on the bottom, 24 on top of those, then 20, and so on.
If there are 108 pieces of wood, how many rows are there? (Hint:n... 7 .)SECTION 12.3 Geometric Sequences 691
Evaluate for the given values of a, r, and n. See Section 5.1.
- 52.a=5, r= n= 2
1
4
a=4, r= n= 3 ,1
2
,
a=2, r=3, n= 2 a=3, r=2, n= 4arnPREVIEW EXERCISES
OBJECTIVES
Geometric Sequences
12.3
1 Find the common
ratio of a geometric
sequence.
2 Find the general
term of a geometric
sequence.
3 Find any specified
term of a geometric
sequence.
4 Find the sum of a
specified number
of terms of a
geometric
sequence.
5 Apply the formula
for the future value
of an ordinary
annuity.
6 Find the sum of an
infinite number of
terms of certain
geometric
sequences.In an arithmetic sequence, each term after the first is found by addinga fixed number
to the previous term. A geometric sequenceis defined as follows.
Geometric SequenceA geometric sequence,or geometric progression,is a sequence in which each
term after the first is found by multiplying the preceding term by a nonzero
constant.
OBJECTIVE 1 Find the common ratio of a geometric sequence.We find
the constant multiplier, called the common ratio,by dividing any term by the
preceding term,.
Common ratioFor example,
Geometric sequenceis a geometric sequence in which the first term, is 2 and the common ratio is
for all n.an+ 1
an