Math Analysis Honors - Worksheet 51
Geometric Series
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Given two terms in a geometric sequence find the explicit formula and the recursive formula.
1) a3 = −50 and a4 = −250
3) a6 = −96 and a3 = 12
2) a2 = −9 and a5 =
1
3
4) a5 = 1024 and a2 = −16
Evaluate each geometric series described.
8
5)
7
Σ3⋅5
k−1
k=1
6)
Σ2⋅5
k−1
k=1
Evaluate the related series of each sequence.
7) −4, −8, −16, −32, −64
8) 1, 5, 25, 125, 625
Evaluate each geometric series described.
9) a1 = −1, r = 4, n = 8
10) a1 = −2, r = −3, n = 9
Determine the number of terms n in each geometric series.
11) a1 = 4, r = −3, S n = −728
12) a1 = −1, r = 2, S n = −15
3
1
21
13) a1 = − , r = , S n = −
5
2
20
14) a1 = −4, r = 5, S n = −124
Determine if each geometric series converges or diverges.
15) 4 − 8 + 16 − 32...
17) 3 + 9 + 27 + 81...
16) 6 + 4 +
8 16
+ ...
3
9
18) −9.5 − 7.6 − 6.08 − 4.864...
Evaluate each infinite geometric series described.
∞
19)
Σ(
n=1
1
−
3
)
∞
n−1
20)
Σ
∞
0.2 ⋅ 0.4 k − 1
k=1
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n−1
n=1
∞
21)
Σ3⋅3
22)
Σ
i=1
()
1
16 ⋅
4
i−1
Worksheet by Kuta Software LLC
Answers to
n−1
1) Explicit: an = −2 ⋅ 5
Recursive: an = an − 1 ⋅ 5
a1 = −2
( )
1
2) Explicit: an = 27 ⋅ −
3
Recursive: an = an − 1 ⋅ −
n−1
3) Explicit: an = 3 ⋅ (−2) n − 1
1
3
Recursive: an = an − 1 ⋅ −2
a1 = 3
a1 = 27
n−1
4) Explicit: an = 4 ⋅ (−4)
Recursive: an = an − 1 ⋅ −4
a1 = 4
7) −124
11) 6
15) Diverges
3
19)
4
5) 292968
8) 781
12) 4
16) Converges
20) No sum
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6) 39062
9) −21845
13) 3
17) Diverges
1
21)
3
10) −9842
14) 3
18) Converges
64
22)
3
Worksheet by Kuta Software LLC