Kuta Software - Infinite Algebra 2

Finite Geometric Series

Evaluate the related series of each sequence.

1)  2,  12,  72,  432

3)  −2,  6,  −18,  54,  −162

Evaluate each geometric series described.

7

k − 1

5)  4

k = 1

9

i − 1

7)  2

i = 1

n − 1

9) 

n = 1

n − 1

n = 1

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Name___________________________________

Date________________  Period____

2)  −1,  5,  −25,  125

4)  −2,  −12,  −72,  −432,  −2592

8

6)  Σ (−6)i − 1

i = 1

9

m − 1

8)  Σ −2

m = 1

n − 1

n  = 1

9

12)  Σ (−2)^{n − 1}

n = 1

-1-

21)  a = −2,  r = 5,  S = −62

                              1                                 n

23)  a = −3,  r = 4,  S = −4095

                              1                                 n

25)  −4 + 16 − 64 + 256...,  S = 52428

n

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22)  a1 = 3,  r = −3,  Sn = −60

24)  a1 = −3,  r = −2,  Sn = 63

n

m − 1

    26)  Σ −2 ⋅ 4     = −42

m = 1

-2-

Kuta Software - Infinite Algebra 2

Finite Geometric Series

Evaluate the related series of each sequence.

1)  2,  12,  72,  432

518

3)  −2,  6,  −18,  54,  −162

−122

Evaluate each geometric series described.

7

k − 1

5)  4

k = 1

5461

9

i − 1

7)  2

i = 1

511

n − 1

9) 

n = 1

−170

n − 1

n = 1

−59048

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Name___________________________________

Date________________  Period____

2)  −1,  5,  −25,  125

104

4)  −2,  −12,  −72,  −432,  −2592

−3110

8

6)  Σ (−6)i − 1

i = 1

−239945

9

m − 1

8)  Σ −2

m  = 1

−511

n − 1

n   = 1

39364

9

12)  Σ (−2)^{n − 1}

n = 1

171

-1-

13)  1 + 2 + 4 + 8...,  n = 6

63

15)  1 − 4 + 16 − 64...,  n = 9

52429

17)  1 − 5 + 25 − 125...,  n = 7

13021

19)  a1 = 4,  an = 1024,  r = −2

684

14)  2 − 10 + 50 − 250...,  n = 8

−130208

16)  −2 − 6 − 18 − 54...,  n = 9

−19682

18)  −3 − 6 − 12 − 24...,  n = 9

−1533

20)    a1 = 4,  an = 8748,  r = 3

13120

Determine the number of terms n in each geometric series.

21)    a = −2,  r = 5,  S = −62     22)  a = 3,  r = −3,  S = −60

                              1                                 n                                                                                                                             1                                 n

                             3                                                                                       4

                 23)  a = −3,  r = 4,  S = −4095                                      24)  a = −3,  r = −2,  S = 63

                              1                                 n                                                                                                                             1                                    n

                             6                                                                                       6

25)  −4 + 16 − 64 + 256...,  S = 52428 n 26)  Σ −2 ⋅ 4 = −42 n                   m − 1

m = 1

8

3

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