Kuta Software - Infinite Precalculus
Name___________________________________
Geometric Sequences and Series
Date________________ Period____
Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the
explicit formula.
1) , , , , ...
3) , , , , ...
2) ,
  
, ,
, ...
  
4) , , , , ...
Given the explicit formula for a geometric sequence find the common ratio, the term named in
the problem, and the recursive formula.


()
5) an
n
6) an()
n
Find a
Find a
Given two terms in a geometric sequence find the common ratio, the explicit formula, and the
recursive formula.
7) a

and a

8) a and a
Find the missing term or terms in each geometric sequence.
9) ..., , ___, ___, , ...
10) ..., , ___, ___, ___, 

, ...

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Worksheet by Kuta Software LLC
Evaluate each geometric series described.
11) ..., n
12) ..., n
13) a, r, n
14) a, r, n

15)



k
16)
k
 


()
m

17)


m

i
18)
i
 
n
n
Determine the number of terms n in each geometric series.

n
19)


i
20) a, r, S n
i
Determine if each geometric series converges or diverges.
21) ...




23)

k
()

22)  ...


k
24)
 
i
i
Evaluate each infinite geometric series described.

25)
(
i


)

27)
(
m


i


26)
 
i
i
)

m
28)
 
k
k
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Name___________________________________
Geometric Sequences and Series
Date________________ Period____
Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the
explicit formula.
1) , , , , ...
2) ,
Common Ratio: r
a
Explicit: an
n
  

, ,
, ... Common Ratio: r
  


a

n

Explicit: an

()
3) , , , , ...
4) , , , , ...
Not geometric
Common Ratio: r
a
Explicit: an
n
Given the explicit formula for a geometric sequence find the common ratio, the term named in
the problem, and the recursive formula.


()
5) an
Find a
n
Common Ratio: r

a



Recursive: anan
a
6) an()
n
Find a
Common Ratio: r
a


Recursive: anan
a
Given two terms in a geometric sequence find the common ratio, the explicit formula, and the
recursive formula.


8) a and a
and a Common Ratio: r


Common Ratio: r
n
n

Explicit: an
Explicit: an 

Recursive: anan

Recursive: anan
a

a
Find the missing term or terms in each geometric sequence.
7) a
( )
9) ..., , ___, ___, , ...
10) ..., , ___, ___, ___, 
, 
, , 

, ...



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Worksheet by Kuta Software LLC
Evaluate each geometric series described.
11) ..., n
12) ..., n


13) a, r, n
14) a, r, n



15)



k
16)
k

m

 
m



17)


()


i
18)
i
 
n
n


Determine the number of terms n in each geometric series.

n
19)


i
20) a, r, S n

i

Determine if each geometric series converges or diverges.
21) ...
Diverges

22)  ...

Converges




23)

k
()

k
24)
 
i
i
Diverges
Converges
Evaluate each infinite geometric series described.

25)
(
i


)

i
26)
i
i




27)
 
(
m



)
m



28)
 
k
k
No sum
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Worksheet by Kuta Software LLC