Find the explicit formula.



Math 442 Practice with sequences and series

?O j2V0q1A3j UK8uGtfaR GSqopfJt6wBaUrteo 6LFLDCC.f L 6Ajlzlw UrdimgshAt1s9 qrfevsDeLrFvCeTdj.5

Find the explicit formula. 1) , , , , ...

3) , , , , ...

Find the recursive formula. 5) , , , , ...

Name___________________________________ Date________________

2) , , , , ... 4) , , , , ...

6) , , , , ...

Given the first term and the common ratio of a geometric sequence find the first five terms.

7) a , r

8) a , r

Given the explicit formula for a geometric sequence find the first five terms.

9) a n n

( ) n

10) a

n

Given the recursive formula for a geometric sequence find the first five terms.

11) a a

n

n

a

12) a a

n

n

a

Given two terms in a geometric sequence find the common ratio.

13) a and a

14) a and a

15) a and a

16) a and a

?3 0220C1x3t XKxuKtMa1 xS4ocfetRwnanrge5 hL6LbCk.U R OA0lrlE xrxiDgLhNtvsp jrcelspehrWv0eldv.m 1 GM7aCd6eH ywViGtVhb 1IPnYfVi2ngiktxeY bAplfgLeYbjrma3 92k.H

-1-

Worksheet by Kuta Software LLC

Given two terms in a geometric sequence find the term named in the problem, the explicit formula, and the recursive formula.

17) a and a

Find a

18) a and a

Find a

19) a and a

Find a

20) a and a

Find a

21) a and a Find a

22) a and a

Find a

Find the missing term or terms in each arithmetic sequence.

23) ..., , ___, ___, ___, ___, , ...

24) ..., , ___, ___, ___, , ...

Find the missing term or terms in each geometric sequence.

25) ..., , ___, ___, ___, , ...

26) ..., , ___, ___, ___, , ...

?I N2j0F1e30 ZKDuothaj 4SmotfdtVwFaorYeQ 1LyLMCZ.r s FAZlDl4 arQiTgmhzt9sl VraeTsdeGrZvdeAdD.l I gMRa4d2ep XwFimtqhs JIenhfsiynMiWtYeB VAXlRghenbQrfaW L2Y.b

-2-

Worksheet by Kuta Software LLC

 Evaluate each arithmetic series described.

27) (i) i

29) (m) m

31) (n) n

33) m m

28) (i) i

30) (i) i

32) (k) k

34) (i) i

35) a , d, n

36) a , d, n

Determine the number of terms n in each arithmetic series.

37) a , a , S

n

n

38) a , a , S

n

n

Evaluate each geometric series described.

39) ()i i

40)

k

k

Determine the number of terms n in each geometric series.

41) a , r, S

n

42) a , r, S

n

?w u2k0i1h3g BKKuotxa1 1S0opfYtow9aEriev xL9LECF.U u aAnl3l8 UrEiTgthqtQsS jroeIsge9rYv3eKdP.3 y yMDavdOei IwVixtChB LI3n1fqi9nkiCtkeF EAqlEgserbaria6 720.q

-3-

Worksheet by Kuta Software LLC

Math 442 Practice with sequences and series

?F a2g0V193u RKqubtMam 5SEo2f3tOwYabrfes xLELwCW.8 6 tAzlFls zriiZgXhJtOs8 YrseSshearyvReodc.0

Name___________________________________ Date________________

Find the explicit formula.

1) , , , , ...

a ()n n

3) , , , , ... a n

n

Find the recursive formula.

2) , , , , ... a n

n

4) , , , , ... a n

n

5) , , , , ...

anan a

6) , , , , ...

anan a

Given the first term and the common ratio of a geometric sequence find the first five terms.

7) a , r , , , ,

8) a , r , , , ,

Given the explicit formula for a geometric sequence find the first five terms.

9) a n n , , , ,

( ) n

10) a

, , , ,

n

Given the recursive formula for a geometric sequence find the first five terms.

11) a a , , , ,

n

n

a

12) a a , , , ,

n

n

a

Given two terms in a geometric sequence find the common ratio.

13) a and a

r

15) a and a

r

14) a and a

r

16) a and a

r

?I U2Y0R1j3q 3Kdu8tXa1 1SOoRfMtZwRaprmeE mLxLeCX.l R rAvlXlN 7rUi5gMhztpsy SrKeUswegrevue7dV.Z O AMPaOdxeS kwRi8txhd YIgnGfhiEnDiCtOev PAKljg7eObirEap f2a.Z

-1-

Worksheet by Kuta Software LLC

Given two terms in a geometric sequence find the term named in the problem, the explicit formula, and the recursive formula.

17) a and a

Find a

a

Explicit: a ()n n

Recursive: a a

n

n

a

18) a and a

Find a

a

Explicit: a ()n n

Recursive: a a

n

n

a

19) a and a

Find a

a

Explicit: a ()n n

Recursive: a a

n

n

a

20) a and a a

Find a

( ) n

Explicit: a

n

Recursive: a a

n

n

a

21) a and a Find a

a

Explicit: a n n

Recursive: a a

n

n

a

22) a and a a

Find a

( ) n

Explicit: a

n

Recursive: a a

n

n

a

Find the missing term or terms in each arithmetic sequence.

23) ..., , ___, ___, ___, ___, , ... , , ,

24) ..., , ___, ___, ___, , ... , ,

Find the missing term or terms in each geometric sequence.

25) ..., , ___, ___, ___, , ... , ,

26) ..., , ___, ___, ___, , ... , ,

?f b2Q0I123n LK8u4tvac sSnoHfMt4whaurjed sLYLrCx.K 2 PAhlilC Cr7iZgEh6tHsG KrCewsyehrFvDebdG.e 3 SMVaCdieb UwKiAtGhB pI1nWffiBnAiyt2eD fAQlVg2eebRrdaQ F2Y.j

-2-

Worksheet by Kuta Software LLC

Evaluate each arithmetic series described.

27) (i) i

29) (m) m

31) (n) n

33) m m

28) (i) i

30) (i) i

32) (k) k

34) (i) i

35) a , d, n

36) a , d, n

Determine the number of terms n in each arithmetic series.

37) a , a , S

n

n

Evaluate each geometric series described.

38) a , a , S

n

n

39) ()i i

40)

k

k

Determine the number of terms n in each geometric series.

41) a , r, S

n

42) a , r, S

n

?o 4270P1R31 zKeudtJar TSSoIfGtMwTaMrsee RLOLiCF.m Y ZARldlc 4rOidgMhCttsi er5eHsFeKrlv3eOdF.g 8 dMFapdreR dwFiLtlh4 6IunufHiBnSiFtZe2 qATlfgveCbNr1aM 22w.y

-3-

Worksheet by Kuta Software LLC

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download