Page 722 - Algebra 1

b. Find the 7th term of geometric sequence. _1 , - _1 , _1 , . . .
SOLUTION
Find the common ratio: -_1 ÷ _1 = -_1 · _3 = -_1. 93913
_1
Raise -3 to the 6th power.
3 927
A(n) = ar n - 1 Use the formula.
_1 ( _1 ) 7 - 1 _1 _1
A(7) = 3-3 _1 ( _1 ) 6
Substitute 7 for n, 3 for a, and -3 for r. Simplify the exponent.
= 3-3 _1 _1
= ()( )
_3 729 1
= 2187
The 7th term in the sequence is _1 .
Multiply.
2187
c. Find the 9th term in the geometric sequence.
17, 8_1, 4_1, 2_1, ... 248
SOLUTION
Findthecommonratio: 8_1 ÷17=_17 ÷17=_17 ·_1 =_1. 2 2 2172
Hint
Choose the two terms that are the easiest for finding the common ratio. Then use that ratio to check.
A(n) = ar n - 1
_1 9-1
Use the formula.
Substitute 9 for n, 17 for a, and 2 for r.
Simplify the exponent.
_1
Raise 2 to the 8th power.
Multiply.
A(9) = 17(2) _1 8
_1
= 17(2) _1
= 17(256 ) = _17
256
The 9th term of the sequence is _17 . 256
d. Find the 5th term of the geometric sequence. 1.2, 7.2, 43.2, ...
SOLUTION
Find the common ratio: 7.2 ÷ 1.2 = 6.
A(n) = arn-1 A(5) = 1.2(6)5-1
Use the formula.
Substitute 5 for n, 1.2 for a, and 6 for r. Simplify.
= 1555.2
The 5th term of the sequence is 1555.2.
Lesson 105 707