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Geometric Sequences (1)

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13.05.2020

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Geometric Sequences (1).pdf

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.

ⁿ − 1 ⁿ − 1

7) a = 3 1

ⁿ8) a = 2 ⋅ ( )

n 4

ⁿ − 1 ⁿ − 1

9) a = −2.5 ⋅ 4 10) a = −4 ⋅ 3

n 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}12) a = a ⋅ −3

n n − 1 n n − 1

a = 2 _a = −3

1 1

13) a = a ^{⋅ 5}14) a = a ⋅ 3

n n − 1 n n − 1

a = 2 _a = −3

1 1

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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 16) a = 1, r = 2

1 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 18) a = 4, r = 6

1 1

19) a = 2, r = 6 20) a = −4, r = 4

1 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 22) a = 4, r = 5

4 1

Given two terms in a geometric sequence find the 8th term and the recursive formula.

23) a = −12 and a = −6 24) a = 768 and a = 12

4 5 5 2

25) a = −2 and a = −512 26) a = 3888 and a = 108

1 5 5 3

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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, ...

r = −6 Not geometric

3) 4, 16, 36, 64, ... 4) −3, −15, −75, −375, ...

Not geometric r = 5

5) −2, −4, −8, −16, ... 6) 1, −5, 25, −125, ...

r = 2 r = −5

Given the explicit formula for a geometric sequence find the first five terms and the 8th term.

n − 1

7) a = 3

First Five Terms: 1, 3, 9, 27, 81

a = 2187

n − 1

8) an = 2 ⋅ ( )

1 1 1 1

First Five Terms: 2, , , ,

2 8 32 128

1 a =

⁸8192

n − 1

9) a = −2.5 ⋅ 4

n − 1

10) a = −4 ⋅ 3

First Five Terms: −4, −12, −36, −108, −324

a = −8748

First Five Terms: −2.5, −10, −40, −160, −640

a = −40960

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

Common Ratio: r = 2

First Five Terms: 2, 4, 8, 16, 32

n − 1

Explicit: a = 2 ⋅ 2

13) a = _a ⋅ 5 n _n − 1

a = 2

Common Ratio: r = 5

First Five Terms: 2, 10, 50, 250, 1250

n − 1

Explicit: a = 2 ⋅ 5

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12) an = an − 1 ⋅ −3 a = −3

Common Ratio: r = −3

First Five Terms: −3, 9, −27, 81, −243

n − 1

Explicit: a = −3 ⋅ (−3)

14) an = an − 1 ⋅ 3 a = −3

Common Ratio: r = 3

First Five Terms: −3, −9, −27, −81, −243

n − 1

Explicit: a = −3 ⋅ 3

-1-

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 16) a = 1, r = 2

1 1

First Five Terms: 0.8, −4, 20, −100, 500 First Five Terms: 1, 2, 4, 8, 16

ⁿ − 1 ⁿ − 1

Explicit: a = 0.8 ⋅ (−5) Explicit: a = 2

n 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) a1 = −4, r = 6 18) a1 = 4, r = 6

Next 3 terms: −24, −144, −864 Next 3 terms: 24, 144, 864

Recursive: ^a_n = ^a_n_{− 1} ⋅ 6 Recursive: ^a_n = ^a_n_{− 1} ⋅ 6

a = −4 a1 = 4

19) a1 = 2, r = 6 20) a1 = −4, r = 4

Next 3 terms: 12, 72, 432 Next 3 terms: −16, −64, −256

Recursive: ^a_n = ^a_n_{− 1} ⋅ 6 Recursive: ^a_n = ^a_n_{− 1} ⋅ 4

a = 2 a = −4

1 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) a4 = 25, r = −5 22) a1 = 4, r = 5

First Five Terms: −0.2, 1, −5, 25, −125 First Five Terms: 4, 20, 100, 500, 2500

n − 1 n − 1

Explicit: a = −0.2 ⋅ (−5) Explicit: an = 4 ⋅ 5

Recursive: ^a_n = ^a_n_{− 1} ⋅ −5 Recursive: ^a_n = ^a_n_{− 1} ⋅ 5

a = −0.2 a = 4

1 1

Given two terms in a geometric sequence find the 8th term and the recursive formula.

23) a₄ = −12 and a₅ = −6

3 a = − 8

24) a₅ = 768 and a₂ = 12

a = 49152

Recursive: a = _a ⋅ 4

_{n n}_{− 1}

Recursive: a = aa = 3

n n − 11

a = −96

25) a1 = −2 and a5 = −512 26) a5 = 3888 and a3 = 108

a = 32768 a = 839808

8 8

Recursive: ^a_n = ^a_n_{− 1} ⋅ −4 Recursive: ^a_n = ^a_n_{− 1} ⋅ 6

a = −2 _a = 3

1 1

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

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Create your own worksheets like this one with

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