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Kuta Software - Infinite Algebra 2 Name___________________________________
Infinite Geometric Series Date________________ Period____
Determine if each geometric series converges or diverges.
1) a1 = −3, r = 4 3
2) a1 = 4, r = −
4
3) a1 = 5.5, r = 0.5 4) a1 = −1, r = 3
5) 81 + 27 + 9 + 3..., 6) 7.1 + 17.75 + 44.375 + 110.9375...,
12 48 192 128 64 32 16
7) −3 + − + ..., 8) − + − ...,
5 25 125 3125 625 125 25
∞ ∞ k − 1
k − 1 16 3
9) Σ−4 10) Σ ( )
k = 1 k = 1 9 2
∞ ∞ k − 1
i − 1 7 1
11) Σ4.2 ⋅ 0.2 12) Σ −
i = 1 k = 1 6( 4)
Evaluate each infinite geometric series described.
1 14) a1 = 1, r = −4
13) a1 = 3, r = −
5
15) a1 = 1, r = −3 1
16) a1 = 1, r =
2
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17) 1 + 0.5 + 0.25 + 0.125..., 9 27 81
18) 3 − + − ...,
4 16 64
19) 81 − 27 + 9 − 3..., 20) 1 − 0.6 + 0.36 − 0.216...,
∞ 1 k − 1 ∞ 1 n − 1
21) Σ5 ⋅ − 22) Σ −6 ⋅ −
k = 1 ( 5) n = 1 ( 2)
∞ i − 1 ∞
1 k − 1
23) Σ( ) 24) Σ4
i = 1 3 k = 1
Determine the common ratio of the infinite geometric series.
25) a1 = 1, S = 1.25 26) a1 = 96, S = 64
16 28) a1 = 1, S = 2.5
27) a1 = −4, S = −
5
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Kuta Software - Infinite Algebra 2 Name___________________________________
Infinite Geometric Series Date________________ Period____
Determine if each geometric series converges or diverges.
1) a1 = −3, r = 4 3
2) a1 = 4, r = −
4
Diverges
Converges
3) a1 = 5.5, r = 0.5 4) a1 = −1, r = 3
Converges Diverges
5) 81 + 27 + 9 + 3..., 6) 7.1 + 17.75 + 44.375 + 110.9375...,
Converges Diverges
12 48 192 128 64 32 16
7) −3 + − + ..., 8) − + − ...,
5 25 125 3125 625 125 25
Converges Diverges
∞ ∞ k − 1
k − 1 16 3
9) Σ−4 10) Σ ( )
k = 1 k = 1 9 2
Diverges Diverges
∞ ∞ k − 1
i − 1 7 1
11) Σ4.2 ⋅ 0.2 12) Σ −
i = 1 k = 1 6( 4)
Converges Converges
Evaluate each infinite geometric series described.
1 14) a1 = 1, r = −4
13) a1 = 3, r = −
5
No sum
5
2
15) a1 = 1, r = −3 1
16) a1 = 1, r =
2
No sum
2
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17) 1 + 0.5 + 0.25 + 0.125..., 9 27 81
18) 3 − + − ...,
2 4 16 64
12
7
19) 81 − 27 + 9 − 3..., 20) 1 − 0.6 + 0.36 − 0.216...,
243 0.625
4
∞ 1 k − 1 ∞ 1 n − 1
21) Σ5 ⋅ − 22) Σ −6 ⋅ −
k = 1 ( 5) n = 1 ( 2)
25 −4
6
∞ i − 1 ∞
1 k − 1
23) Σ( ) 24) Σ4
i = 1 3 k = 1
3 No sum
2
Determine the common ratio of the infinite geometric series.
25) a1 = 1, S = 1.25 26) a1 = 96, S = 64
0.2 1
−
2
16 28) a1 = 1, S = 2.5
27) a1 = −4, S = −
5
0.6
1
−
4
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Infinite Algebra 2
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