Geometric Sequences Date Period
Kuta Software - Infinite Algebra 2
Name___________________________________
Geometric Sequences
Date________________ Period____
Determine if the sequence is geometric. If it is, find the common ratio.
1) -1, 6, -36, 216, ...
2) -1, 1, 4, 8, ...
3) 4, 16, 36, 64, ...
4) -3, -15, -75, -375, ...
5) -2, -4, -8, -16, ...
6) 1, -5, 25, -125, ...
Given the explicit formula for a geometric sequence find the first five terms and the 8th term.
7) a = 3n - 1 n
( )1 n - 1
8) a = 2
n
4
9) a = -2.5 4n - 1 n
10) a = -4 3n - 1 n
Given the recursive formula for a geometric sequence find the common ratio, the first five terms, and the explicit formula.
11) a = a 2 n n-1 a =2 1
12) a = a -3
n
n - 1
a = -3 1
13) a = a 5 n n-1 a =2 1
14) a = a 3
n
n - 1
a = -3 1
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-1-
Worksheet by Kuta Software LLC
Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula.
15) a = 0.8, r = -5 1
16) a = 1, r = 2 1
Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given.
17) a = -4, r = 6 1
18) a = 4, r = 6 1
19) a = 2, r = 6 1
20) a = -4, r = 4 1
Given a term in a geometric sequence and the common ratio find the first five terms, the explicit formula, and the recursive formula.
21) a = 25, r = -5 4
22) a = 4, r = 5 1
Given two terms in a geometric sequence find the 8th term and the recursive formula.
23) a = -12 and a = -6
4
5
24) a = 768 and a = 12
5
2
25) a = -2 and a = -512
1
5
26) a = 3888 and a = 108
5
3
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Geometric Sequences
Date________________ Period____
Determine if the sequence is geometric. If it is, find the common ratio.
1) -1, 6, -36, 216, ... r = -6
2) -1, 1, 4, 8, ... Not geometric
3) 4, 16, 36, 64, ... Not geometric
4) -3, -15, -75, -375, ... r = 5
5) -2, -4, -8, -16, ... r = 2
6) 1, -5, 25, -125, ... r = -5
Given the explicit formula for a geometric sequence find the first five terms and the 8th term.
7) a = 3n - 1 n
First Five Terms: 1, 3, 9, 27, 81 a = 2187
8
( )1 n - 1
8) a = 2
n
4
11 1 1 First Five Terms: 2, , , ,
2 8 32 128
1 a=
8 8192
9) a = -2.5 4n - 1 n
10) a = -4 3n - 1 n
First Five Terms: -2.5, -10, -40, -160, -640 a = -40960
8
First Five Terms: -4, -12, -36, -108, -324 a = -8748
8
Given the recursive formula for a geometric sequence find the common ratio, the first five terms, and the explicit formula.
11) a = a 2 n n-1 a =2 1
Common Ratio: r = 2 First Five Terms: 2, 4, 8, 16, 32 Explicit: a = 2 2n - 1
n
12) a = a -3
n
n - 1
a = -3 1
Common Ratio: r = -3 First Five Terms: -3, 9, -27, 81, -243
Explicit: a = -3 (-3)n - 1 n
13) a = a 5 n n-1 a =2 1
Common Ratio: r = 5 First Five Terms: 2, 10, 50, 250, 1250 Explicit: a = 2 5n - 1
n
14) a = a 3
n
n - 1
a = -3 1
Common Ratio: r = 3
First Five Terms: -3, -9, -27, -81, -243
Explicit: a = -3 3n - 1 n
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-1-
Worksheet by Kuta Software LLC
Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula.
15) a = 0.8, r = -5 1
First Five Terms: 0.8, -4, 20, -100, 500
Explicit: a = 0.8 (-5)n - 1 n
16) a = 1, r = 2 1
First Five Terms: 1, 2, 4, 8, 16 Explicit: a = 2n - 1
n
Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given.
17) a = -4, r = 6 1
Next 3 terms: -24, -144, -864
Recursive: a = a 6
n
n - 1
a = -4 1
18) a = 4, r = 6 1
Next 3 terms: 24, 144, 864
Recursive: a = a 6
n
n - 1
a =4 1
19) a = 2, r = 6 1
Next 3 terms: 12, 72, 432
Recursive: a = a 6
n
n - 1
a =2 1
20) a = -4, r = 4 1
Next 3 terms: -16, -64, -256
Recursive: a = a 4
n
n - 1
a = -4 1
Given a term in a geometric sequence and the common ratio find the first five terms, the explicit formula, and the recursive formula.
21) a = 25, r = -5 4
First Five Terms: -0.2, 1, -5, 25, -125
Explicit: a = -0.2 (-5)n - 1 n
Recursive: a = a -5
n
n - 1
a = -0.2 1
22) a = 4, r = 5 1
First Five Terms: 4, 20, 100, 500, 2500
Explicit: a = 4 5n - 1 n
Recursive: a = a 5
n
n - 1
a =4 1
Given two terms in a geometric sequence find the 8th term and the recursive formula.
23) a = -12 and a = -6
4
5
3 a =- 8 4
1
Recursive: a = a
2 n
n - 1
a = -96 1
25) a = -2 and a = -512
1
5
a = 32768 8
Recursive: a = a -4
n
n - 1
a = -2 1
24) a = 768 and a = 12
5
2
a = 49152 8
Recursive: a = a 4
n
n - 1
a =3 1
26) a = 3888 and a = 108
5
3
a = 839808 8
Recursive: a = a 6
n
n - 1
a =3 1
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-2-
Worksheet by Kuta Software LLC
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