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Advanced Algebra Prep – Arithmetic Sequences Name___________________________________

Show formulas and work for each problem! Date________________ Period____

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Determine if the sequence is arithmetic. If it is, find the common difference.

1) −38, −68, −98, −128, … 2) 7, 11, 15, 19, …

3) −1, 99, 199, 299, … 4) −37, −33, −29, −25, …

Find the explicit formula and the recursive formula.

5) 38, 238, 438, 638, … 6) 13, 213, 413, 613, …

7) −19, −28, −37, −46, … 8) −31, −29, −27, −25, …

Given the first term and the common difference of an arithmetic sequence find the 52nd term and the

explicit formula.

1 3

9) a1 = 1, d = 10) a1 = 3, d =

2 2

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Given a term in an arithmetic sequence and the common difference find the term named in the problem.

11) a18 = 84, d = 4 12) a26 = −5009, d = −200

Find a39 Find a29

Given a term in an arithmetic sequence and the common difference find the explicit formula.

13) a28 = 75, d = 4

Given two terms in an arithmetic sequence find the term named in the problem.

14) a16 = −83 and a39 = −152 15) a16 = −419 and a38 = −1079

Find a26 Find a31

16) a15 = 146 and a37 = 366 17) a18 = −196 and a37 = −386

Find a23 Find a24

Given two terms in an arithmetic sequence find the explicit formula.

18) a10 = −9 and a30 = −109

Given two terms in an arithmetic sequence find the common difference.

19) a16 = −56 and a33 = −141 20) a16 = 24 and a36 = 64

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Answers to Show formulas and work for each problem!

1) d = −30 2) d = 4 3) d = 100 4) d = 4

5) Explicit: an = −162 + 200n 6) Explicit: an = −187 + 200n 7) Explicit: an = −10 − 9n

Recursive: an = an − 1 + 200 Recursive: an = an − 1 + 200 Recursive: an = an − 1 − 9

a1 = 38 a1 = 13 a1 = −19

8) Explicit: an = −33 + 2n 53 159

9) a52 = 10) a52 =

Recursive: an = an − 1 + 2 2 2

a1 = −31 1 1 3 3

Explicit: an = + n Explicit: an = + n

2 2 2 2

11) a39 = 168 12) a29 = −5609 13) an = −37 + 4n 14) a26 = −113

15) a31 = −869 16) a23 = 226 17) a24 = −256 18) an = 41 − 5n

19) d = −5 20) d = 2

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