Geometric Sequences and Series

(1)

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Precalculus

Geometric Sequences and Series

Name___________________________________

Date________________ Period____

-1-

Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.

1) , , , , ...

2) , 

, 

, 

, ...

3) , , , , ... 4) , , , , ...

Given the explicit formula for a geometric sequence find the common ratio, the term named in the problem, and the recursive formula.

5) a

n

(

^

)

^{n}

Find a_

6) a

n

(



)

^{n}

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) ..., , ___, ___, ___,  

, ...

(2)

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-2-

Evaluate each geometric series described.

11) ..., n 12) ..., n

13) a_, r, n 14) a_, r, n

15)



_{k}^ ^{}^{k} ¹⁶⁾_{m}



^ ^{}

(

^

)

^{m}

17)



_{i}^ ^{}^{i} ¹⁸⁾



_{n}^ ^{}^{n}

Determine the number of terms n in each geometric series.

19)



_{i}ⁿ ^^{i}^{} ^{20) a}^, r, S_n

Determine if each geometric series converges or diverges.

21) ...

22) 

...

23)



_{k}^ ^{}

(

^

)

^{k} ²⁴⁾

^

^{i}^ ^{}^{i}

Evaluate each infinite geometric series described.

25)



_{i}^

(

^

)

^{i} ²⁶⁾

^

^{i}^ ^{}^{i}

27) _{m}



^

(

^^

)

^{m} ²⁸⁾

^

^{k}^ ^^{k}

(3)

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Kuta Software - Infinite Precalculus

Geometric Sequences and Series

Name___________________________________

Date________________ Period____

-1-

Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula.

1) , , , , ...

Common Ratio: r

a_

Explicit: a_n^{n}

2) , 

, 

, 

, ... Common Ratio: r

 a_ 



Explicit: a

n

(

^

)

^{n}

3) , , , , ...

Not geometric

4) , , , , ...

Common Ratio: r

a_

Explicit: a

n^{n}

Given the explicit formula for a geometric sequence find the common ratio, the term named in the problem, and the recursive formula.

5) a

n

(

^

)

^{n}

Find a_

Common Ratio: r

 a_ 



Recursive: a

na_{n}

 a_

6) a

n

(



)

^{n}

Find a_

Common Ratio: r

a_

Recursive: a_na_{n}

a_

Given two terms in a geometric sequence find the common ratio, the explicit formula, and the recursive formula.

7) a_

 and a_ Common Ratio: r

 Explicit: a

n

(

^^

)

^{n}

Recursive: a_na_{n} 

 a_

8) a_ and a_

Common Ratio: r

Explicit: a_n^{n}

Recursive: a_na_{n}

a_

Find the missing term or terms in each geometric sequence.

9) ..., , ___, ___, , ...

,  10) ..., , ___, ___, ___,  

, ...

, , 



(4)

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-2-

Evaluate each geometric series described.

11) ..., n



12) ..., n



13) a_, r, n



14) a_, r, n



15)



_{k}^ ^{}^{k}



16) _{m}



^ ^{}

(

^

)

^{m}





17)



_{i}^ ^{}^{i}



18)



_{n}^ ^{}^{n}



Determine the number of terms n in each geometric series.

19)



_{i}ⁿ ^^{i}^{}



20) a_, r, S_n



Determine if each geometric series converges or diverges.

21) ...

Diverges

22) 

...

Converges

23)



_{k}^ ^{}

(

^

)

^{k}

Converges

24)



_{i}^ ^{}^{i}

Diverges Evaluate each infinite geometric series described.

25)



_{i}^

(

^

)

^{i}





26)



_{i}^ ^{}^{i}



27) _{m}



^

(

^^

)

^{m} ^ 28)



_{k}^ ^^{k}

No sum

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