Arithmetic Sequences and Series

(1)

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Precalculus

Arithmetic Sequences and Series

Name___________________________________

Date________________ Period____

-1-

Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the explicit formula, and the three terms in the sequence after the last one given.

1) , , , , ... 2) , , , , ...

3) , 

, , 

, ... 4) , , , , ...

Given the explicit formula for an arithmetic sequence find the common difference, 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 an arithmetic sequence find the common difference, the explicit formula, and the recursive formula.

7) a_ and a_ 8) a_ and a_

Find the missing terms in each arithmetic sequence.

9) ..., 

, ___, ___, , ... 10) ..., , ___, ___, , ...

(2)

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-2-

Evaluate the related series of each sequence.

11) , , ,  12) , , , , , , 

Evaluate each arithmetic series described.

13) a_

, d

, n 14) a_, d, n

15) a_, a

n, n 16) a_, a

n, n

17) _{m}



^

(

^{}^m

)

¹⁸⁾

^

n



(

n

)

19) _{m}



^

⁽

^{m}

⁾

²⁰⁾



_{k}^

(

^^ 

k

)

21)



_{i}^

⁽

^{i}

⁾

²²⁾



_{n}^

⁽

^{n}

⁾

Determine the number of terms n in each arithmetic series.

23) 

(



)



(



)



(



)

..., S_n 24) ..., S_n

(3)

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Kuta Software - Infinite Precalculus

Arithmetic Sequences and Series

Name___________________________________

Date________________ Period____

-1-

Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, the explicit formula, and the three terms in the sequence after the last one given.

1) , , , , ...

Common Difference: d

Next 3 terms: , , 

a_

Explicit: a_nn

2) , , , , ...

Not arithmetic

3) , 

, , 

, ... Common Difference: d

 Next 3 terms: , 

,  a_

 Explicit: a

n

 

n

4) , , , , ...

Common Difference: d

Next 3 terms: , , 

a_

Explicit: a

nn

Given the explicit formula for an arithmetic sequence find the common difference, the term named in the problem, and the recursive formula.

5) a

nn Find a_

Common Difference: d

a_

Recursive: a

na_{n}

a_

6) a

n

 

n Find a_

Common Difference: d

 a_

 Recursive: a

na_{n}

 a_

Given two terms in an arithmetic sequence find the common difference, the explicit formula, and the recursive formula.

7) a_ and a_

Common Difference: d

Explicit: a

nn

Recursive: a_na_{n}

a_

8) a_ and a_

Common Difference: d

Explicit: a

nn Recursive: a_na_{n}

a_

Find the missing terms in each arithmetic sequence.

9) ..., 

, ___, ___, , ... , 



10) ..., , ___, ___, , ...

, 

(4)

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-2-

Evaluate the related series of each sequence.

11) , , , 



12) , , , , , , 



Evaluate each arithmetic series described.

13) a_

, d

, n





14) a_, d, n



15) a_, a

n, n



16) a_, a

n, n



17) _{m}



^

(

^{}^m

)





18)



_{n}^

⁽

^{n}

⁾



19) _{m}



^

⁽

^{m}

⁾



20)



_{k}^

(

^^ 

k

)





21)



_{i}^

⁽

^{i}

⁾



22)



_{n}^

⁽

^{n}

⁾



Determine the number of terms n in each arithmetic series.

23) 

(



)



(



)



(



)

..., S_n



24) ..., S_n



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