Sequences and Series

(1)

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Precalculus

Sequences and Series

Name___________________________________

Date________________ Period____

-1-

Find the next three terms in each sequence.

1) , , , , , ... 2) , , , , , ...

Find the first four terms in each sequence.

3) a_n^{n} 4) a

n  n

5) a_na_{n}

a_

6) a_na_{n}

a_

Find the tenth term in each sequence.

7) a_n

n

8) a

na_{n}n a_

Determine if each sequence converges or diverges.

9) , , , , , ... 10) , , , , , ...

11) a_n  n

12) a

n

(



)

^{n}

13) a

na_{n}

a_ 14) a_na_{n}

 a_

(2)

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-2-

Rewrite each series as a sum.

15)



_{n}^

⁽

^{n}^

⁾

¹⁶⁾



_{n}^

⁽

^{n}

⁾

17) _{m}



^ _^^m ¹⁸⁾



_{a}^ ^a^^_a

Evaluate each series.

19) _{m}



^

⁽

^{m}

⁾

²⁰⁾



_{n}^ ^_n

21)



_{k}^ ^_k ²²⁾



_{n}^

⁽

^{n}

⁾

23)



_{k}^

⁽

^{k}^

⁾

²⁴⁾



_{n}^ ⁿ

25)



_{n}^ ^_n ²⁶⁾



_{a}^ _{a}^a

Rewrite each series using sigma notation.

27) 

28) 









29) 



 

 

 

 



30) 

31) 











32) 

(3)

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Kuta Software - Infinite Precalculus

Sequences and Series

Name___________________________________

Date________________ Period____

-1-

Find the next three terms in each sequence.

1) , , , , , ...

, , 

2) , , , , , ...

, , 

Find the first four terms in each sequence.

3) a_n^{n}

, , , 

4) a

n  n



, 

, , 

 5) a_na_{n}

a_

, , , 

6) a_na_{n}

a_

, , , 

Find the tenth term in each sequence.

7) a_n

n a_



8) a

na_{n}n a_

a_

Determine if each sequence converges or diverges.

9) , , , , , ...

Converges

10) , , , , , ...

Diverges

11) a_n  n

Converges

12) a

n

(



)

^{n}

Diverges

13) a

na_{n}

a_

Diverges

14) a_na_{n}

 a_

Converges

(4)

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-2-

Rewrite each series as a sum.

15)



_{n}^

⁽

^{n}^

⁾



16)



_{n}^

⁽

^{n}

⁾



17) _{m}



^ _^^m





 

 



18)



_{a}^ ^a^^_a





 

 

 

 Evaluate each series.

19) _{m}



^

⁽

^{m}

⁾



20)



_{n}^ ^_n





21)



_{k}^ ^_k



22)



_{n}^

⁽

^{n}

⁾



23)



_{k}^

⁽

^{k}^

⁾



24)



_{n}^ ⁿ



25)



_{n}^ ^_n





26)



_{a}^ _{a}^a





Rewrite each series using sigma notation.

27)  _{m}



^ ^m^ _{28) }^











_{k}^ ^_k

29) 



 

 

 

 





_{k}^ _^^k 30) 



_{n}^ ^n

31) 













_{a}^ _{a}^a 32) 



_{a}^ ^^a

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